PSG star Mbappe came in as a second-half replacement for Antoine Griezmann at the Ernst Happel Stadium in Vienna and burst through in characteristic fashion for the 83rd-minute leveller, cancelling out Andreas Weimann's goal.
The result leaves France, who won last year's edition of the Nations League, winless three games into the tournament.
Mbappe had a great opportunity to give Les Bleus all three points with three minutes left, only for his attempt to rattle the crossbar.
"I'm disappointed that we didn't score more with all the chances we had," said France coach Didier Deschamps.
"Sometimes we score more goals with less opportunities but I'm not worried. I've had to do with minor injuries and fatigue."
After a 1-0 defeat against Denmark at home and a 1-1 draw in Croatia, Deschamps reshuffled his team as he looked to rest some key players at the end of a long and demanding season.
“We had so many chances in the second half. We had the control of the game but we weren’t efficient enough,” Deschamps added. “These aren’t the results we expected. But obviously we’re not in our best form.”
France looked fragile in the first half, and fell behind when striker Weimann put former Manchester United interim coach Ralf Rangnick’s side ahead in the 37th minute.
Liverpool’s Ibrahima Konate made his France debut in the centre of defence. But he was far too static on Austria’s goal, as Marko Arnautovic's cross was swept in by Weimann.
Karim Benzema, who scored minutes into his international debut against Austria in 2007, earlier had a close-range header saved by goalkeeper Patrick Pentz.
Pentz then kept out Benzema’s curler and a shot from Benjamin Pavard as Les Bleus hit back.
Mbappe came on in the 63rd for the ineffective Griezmann, who has not scored for Atletico Madrid or France since early January.
Only the group winners make it to the final four, while the last-placed teams will be relegated.
Meanwhile, an opportunist second-half goal from Mario Pasalic gave Croatia a 1-0 away win in Denmark in the Nations League as playmaker Luka Modric came off the bench to turn the game around for the visitors.
Following his halftime introduction, Modric took the corner that was worked into the box for Pasalic to pounce on for the only goal of the game, slotting the ball through the legs of keeper Kasper Schmeichel.