Medical staff treated the Dons defender for eight minutes in Sunday's League Cup semi-final victory after a collision during an aerial challenge.
He was taken to hospital and the Scottish side went on to win 1-0.
The 31-year-old has now returned to his club but is likely to miss Wednesday's Premiership match with Hamilton.
The Dons are eighth in the league and will face holders Celtic in December's League Cup final.
"We can confirm that the injury sustained by Andrew Considine yesterday was not as serious as first thought," Aberdeen said in a statement.