Cover	Mar. 24, 2023
Cover [Abstract]
Document Type	8-K
Amendment Flag	false
Document Period End Date	Mar. 24, 2023
Current Fiscal Year End Date	--11-30
Entity File Number	811-21593
Entity Registrant Name	Kayne Anderson Energy Infrastructure Fund, Inc.
Entity Central Index Key	0001293613
Entity Tax Identification Number	56-2474626
Entity Incorporation, State or Country Code	MD
Entity Address, Address Line One	811 Main Street
Entity Address, Address Line Two	14th Floor
Entity Address, City or Town	Houston
Entity Address, State or Province	TX
Entity Address, Postal Zip Code	77002
City Area Code	877
Local Phone Number	657-3863
Written Communications	false
Soliciting Material	false
Pre-commencement Tender Offer	false
Pre-commencement Issuer Tender Offer	false
Entity Emerging Growth Company	false