The Gunners currently sit fifth in the table, two points back from fourth-placed Liverpool.
And they still have to play Manchester City, Tottenham and Manchester United before the end of the season.
Arsenal have secured European qualification each year since Arsene Wenger took charge in north London.
But Henry is concerned his old side may not be playing in the continent’s elite club tournament come September.
The Arsenal legend told The Sun: “There is all the talk about Arsene’s future. But the focus now should be saving the season and the top four.
“It won’t be easy. I’ve never been as worried about us falling out of the top four as I am now.”
Arsenal are back in top flight action when they play West Brom on Saturday March 18.
First up though is tomorrow’s FA Cup sixth-round showdown with non-league Lincoln City.