Essien, 23, will miss both legs of Chelsea knockout stage match.
They will find out who they play when the draw is made tomorrow.
He was charged with gross unsporting conduct for the challenge in last week's 0-0 draw at the Bridge.
The Ghana midfielder has since apologised to Hamann for the tackle.
"Michael has spoken to Dietmar by telephone," said a Chelsea spokesman.
"He apologised to Dietmar, assured him the tackle was accidental and that there was no malicious intent."
Essien caught Hamann just below the knee but the tackle was missed by the referee.