The manager is also said to have had coins thrown at him during the League Cup semi-final against Aberdeen and St Johnstone at Tynecastle.
A spokeswoman for Police Scotland told the Evening Times yesterday they had not received any complaints following the match in Edinburgh on Saturday.
But in a statement on the Aberdeen website, a spokesman for the club said: "The support we enjoyed at Tynecastle was absolutely fantastic and helped to create an incredible atmosphere that the manager and players acknowledged played a major part in what was wonderful day and occasion for Aberdeen Football Club.
"However, it would appear that a tiny minority within the main stand behaved in a manner that is completely unacceptable and has absolutely no place in football and we would urge anyone who has any information as to the identity of those responsible to get in touch with the club in order that appropriate action can be taken."
It is understood Lennon walked out of the stadium shortly after Adam Rooney scored the third goal in the 62nd minute of Aberdeen's 4-0 victory.
Lennon was sitting in the main stand at Tynecastle, close to Aberdeen fans.
Celtic hit out at the behaviour of some supporters in the stand.
A club spokesman said it was "totally unacceptable" for the Celtic manager to be treated in such a way.
A spokeswoman from Police Scotland said: "Police in Edinburgh have received no reports relating to assaults of abuse of anyone associated with Celtic Football Club or Hearts Midlothian Football Club following the match at Tynecastle on Saturday, February 1."
Police Scotland can be contacted on 101.