Document And Entity Information	12 Months Ended
Nov. 30, 2025
Document Information [Line Items]
Entity Central Index Key	0001293613
Document Type	N-CSR
Entity Registrant Name	KAYNE ANDERSON ENERGY INFRASTRUCTURE FUND, INC.
Document Period End Date	Nov. 30, 2025
Amendment Flag	false

Boolean flag that is true when the XBRL content amends previously-filed or accepted submission.

No definition available.

Name:	dei_AmendmentFlag
Namespace Prefix:	dei_
Data Type:	xbrli:booleanItemType
Balance Type:	na
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	dei_DocumentInformationLineItems
Namespace Prefix:	dei_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

For the EDGAR submission types of Form 8-K: the date of the report, the date of the earliest event reported; for the EDGAR submission types of Form N-1A: the filing date; for all other submission types: the end of the reporting or transition period. The format of the date is YYYY-MM-DD.

+ References

No definition available.

+ Details

Name:	dei_DocumentPeriodEndDate
Namespace Prefix:	dei_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

- Definition

The type of document being provided (such as 10-K, 10-Q, 485BPOS, etc). The document type is limited to the same value as the supporting SEC submission type, or the word 'Other'.

+ References

No definition available.

+ Details

Name:	dei_DocumentType
Namespace Prefix:	dei_
Data Type:	dei:submissionTypeItemType
Balance Type:	na
Period Type:	duration

- Definition

A unique 10-digit SEC-issued value to identify entities that have filed disclosures with the SEC. It is commonly abbreviated as CIK.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Exchange Act
-Number 240
-Section 12
-Subsection b-2

+ Details

Name:	dei_EntityCentralIndexKey
Namespace Prefix:	dei_
Data Type:	dei:centralIndexKeyItemType
Balance Type:	na
Period Type:	duration

- Definition

The exact name of the entity filing the report as specified in its charter, which is required by forms filed with the SEC.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Exchange Act
-Number 240
-Section 12
-Subsection b-2

+ Details

Name:	dei_EntityRegistrantName
Namespace Prefix:	dei_
Data Type:	xbrli:normalizedStringItemType
Balance Type:	na
Period Type:	duration