Fulton County jail records show Abraham was in jail pending bond of $7,000, or $3,500 for each of the obstruction charges.
WAGA-TV reports Abraham allegedly entered a taped-off area where a woman was threatening to jump off a building. Abraham was arrested after refusing to leave the area.
The arrest of Abraham, the team's top pass rusher, comes one week after running back Michael Turner's drunken driving arrest. Turner was allowed to play in Sunday's 27-3 win in San Diego.
The Falcons issued a statement Monday night, saying the team was aware of "the news regarding John Abraham" and was gathering information.