The pair clashed just two minutes into Sunday’s Edinburgh derby clash at Easter Road.
Eckersley appeared to motion his head towards Allan’s face during the newly-crowned Scottish Championship winners’ 2-0 defeat by Hibs.
Scottish Football Association compliance officer Tony McGlennan has issued the player with a Notice of Complaint.
The 29-year-old former Manchester United youth is accused of breaching Disciplinary Rule 200 after committing an act of “violent conduct by head-butting Scott Allan of Hibernian FC”.
Eckersley has been offered a fixed two-game suspension to be served immediately.
If he accepts the charge, he would miss Saturday’s Tynecastle clash with Raith Rovers and then Hearts’ final away game of the season at Cowdenbeath before returning in time to face Rangers on the final day of the campaign.
He has until 3pm on Wednesday to respond to the complaint, while a principal hearing, if it is required, has been set for tomorrow.