They added that the 54-year-old Dimitrelos, who was taken into custody voluntarily, is due to testify before the public prosecutor on Friday.
AEK said the alleged offences occurred before Dimitrelos' tenure at the club, which started last year, and said the tax arrears were being settled under a debt restructuring procedure initiated by the club under the country's bankruptcy code.
"The voluntary attendance of our president Andreas Dimitrelos at police headquarters concerns club debts from previous administrations which have been restructured by Article 44 (of the bankruptcy code) and for which the present administration is not liable as they have not arisen out of the current fiscal year," AEK said in a statement.
"On the contrary, up to this point Mr Dimitrelos has managed to keep AEK Athens alive, so much so that we are all united in the hope for our final victory and salvation."
Athens public prosecutor Grigoris Peponis has also issued warrants for the arrest of the club's presidents from 2004 to October 2012, including former AEK and Greece striker Demis Nikolaidis, who was president from 2004-2008, plus Giorgos Kintis, Nikos Thanopoulos and Stavros Adamidis.
AEK are 11th in the 16-team Greek Super League after their worst start to a season characterised by financial struggles.
The club has been operating on a shoe-string budget following a period of financial turmoil in which almost the entire first-team squad was sold last year to secure a Super League licence and preserve the team's top-flight status.
Dimitrelos' arrest is the latest setback for AEK following the life ban from international football imposed on midfielder Giorgos Katidis by the Greek football federation (EPO) after he made a Nazi salute to fans to celebrate a goal.
The 20-year-old former Greece under-19 captain made the gesture after scoring the winner in a 2-1 league victory over lowly Veria last Saturday.
The club suspended him for the rest of the season after he apologised and asked to be dropped from the first team.
($1 = 0.7737 euros)