Accrued Expenses and Current Portion of Other Long-Term Liabilities (Narrative) (Details) - USD ($)	3 Months Ended	6 Months Ended
Mar. 29, 2025	Mar. 30, 2024	Mar. 29, 2025	Mar. 30, 2024	Sep. 28, 2024
Accrued Expenses and Current Portion of Other Long-Term Liabilities [Abstract]
Workers' compensation per occurrence covered under insurance cost	$ 1,000,000.0		$ 1,000,000.0
Medical care benefits per person covered under insurance cost	500,000		500,000
Self insurance liabilities	37,300,000		37,300,000		$ 35,900,000
Self insurance liabilities, current	16,900,000		16,900,000		16,500,000
Self insurance liabilities, noncurrent	20,400,000		20,400,000		19,400,000
Receivable for expected self-insurance recoveries from excess cost insurance	3,700,000		3,700,000		$ 4,100,000
Employee insurance expense	$ 12,000,000.0	$ 9,400,000	$ 23,200,000	$ 22,400,000

Medical care benefits insurance liability per person.

No definition available.

Name:	imkta_MedicalCareBenefitsInsuranceLiabilityPerPerson
Namespace Prefix:	imkta_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Carrying amount as of the balance sheet date of amounts expected to be recovered under the terms of insurance contracts.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(17))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_EstimatedInsuranceRecoveries
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

The expense in the period incurred with respect to protection provided by insurance entities against risks other than risks associated with production (which are allocated to cost of sales).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483621/220-10-S99-2

+ Details

Name:	us-gaap_GeneralInsuranceExpense
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- References

No definition available.

+ Details

Name:	us-gaap_PayablesAndAccrualsAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Carrying amount (including both current and noncurrent portions) of accrued known and estimated losses incurred as of the balance sheet date for which no insurance coverage exists, and for which a claim has been made or is probable of being asserted, typically arising from workmen's compensation-type of incidents and personal injury to nonemployees from accidents on the entity's property.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(24))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_SelfInsuranceReserve
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Carrying amount of accrued known and estimated losses incurred as of the balance sheet date for which no insurance coverage exists, and for which a claim has been made or is probable of being asserted, typically arising from workmen's compensation-type of incidents and personal injury to nonemployees from accidents on the entity's property that are expected to be paid within one year (or the normal operating cycle, if longer).

+ References

No definition available.

+ Details

Name:	us-gaap_SelfInsuranceReserveCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Carrying amount of accrued known and estimated losses incurred as of the balance sheet date for which no insurance coverage exists, and for which a claim has been made or is probable of being asserted, typically arising from workmen's compensation-type of incidents and personal injury to nonemployees from accidents on the entity's property that are expected to be paid after one year (or the normal operating cycle, if longer).

+ References

No definition available.

+ Details

Name:	us-gaap_SelfInsuranceReserveNoncurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Carrying value as of the balance sheet date of obligations and payables pertaining to claims incurred of a workers compensation nature. Used to reflect the current portion of the liabilities (due within one year or within the normal operating cycle if longer).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(20))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_WorkersCompensationLiabilityCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant