The 37-year-old’s final match was a 2-2 draw on Saturday which meant the Red Bulls were beaten 4-3 on aggregate by New England Revolution in the Eastern Conference Championship play-off.
“The decision has always been that I would leave after the duration of my contract,” Frenchman Henry said.
“I’ll take the next few weeks to decide on the next chapter of my career.”
Henry won the World Cup with France in 1998 and two Premier League titles with the Gunners, where he played between 1999 and 2007.
He added the Champions League with Barcelona in 2009 and returned to Arsenal for four matches on loan in 2012, coming on as a substitute to score the winner against Leeds in the third round of the FA Cup.
In an interview with French newspaper L’Equipe last month, Henry hinted at another return to the Emirates and said: “One thing is certain: I will stay in football, as a coach, a consultant or executive. We will see.
“The second certainty is that I would love to see Arsenal win the Champions League. Whether that is from near or far does not depend on me, but it is sure I’d like to help. This is my club and, as a player, I was not able to give them the Champions League.”
Source: BBC Sport