With the game scoreless at the time, the Liverpool captain attempted to chase down Mesut Ozil on an Arsenal counterattack only to pull up lame as he closed the attacker down.
Henderson limped on as play continued. He went down on the next stoppage and looked to be grabbing his hamstring.
He was replaced by James Milner.
Henderson has started 14 of Liverpool's Premier League games this season, scoring a goal and adding an assist.
The Reds captain had been restored to the starting line-up after being rested for Liverpool's 4-0 win over Bournemouth.
Liverpool, who entered the contest in fourth place in the Premier League, have a busy slate of fixtures upcoming.
Jurgen Klopp should have Adam Lallana to call upon, though, after the midfielder made his latest comeback off the bench against Bournemouth.