Joachim Low's Germany secured qualification to next summer's World Cup in midweek with a 3-1 victory over Northern Ireland, and will be defending their crown in Russian Federation.
"With Mustafi it seems that it is some muscle tear or some muscle fibre tear", Low said.
Mustafi's injury was the only blotch on another winning night for the world champions with qualification for Russian Federation already in the bag.
The victory came at the cost of two centre-backs, as Bayern Munich's Niklas Suele and Arsenal's Shkodran Mustafi both limped off with first-half injuries.
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The Chargers did, and Henry's spike following his 25-yard touchdown reception helps sum up how bad the team needed this win. A source told ESPN that Beckham will get a second opinion before deciding on surgery to fix the injury.
It means the Germans end their qualifying campaign with a ideal record of 10 wins, scoring 43 and conceding just four.
With Mustafi down, Azerbaijan continued their attack which led to them scoring a goal courtesy of Ramil Sheydaev.
Joachim Low's side found their feet after the break with Liverpool midfielder Emre Can among the scorers.
Germany was without Real Madrid midfielder Toni Kroos, who was allowed to return to Spain to fully heal a rib injury, and Paris Saint-Germain midfielder Julian Draxler, who had an illness.
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Leon Goretzka had earlier given Germany the lead on nine minutes. Shkodran Mustafi pulled up with an apparent thigh injury and was unable to follow Sheydaev, who eluded Antonio Ruediger and beat Bernd Leno at his near post. Goal-line technology confirmed the ball crossed the line before Ruslan Abisov's headed clearance.
Goretzka grabbed Germany's fourth just two minutes later when he fired home Leroy Sane's pass after some good work by the Manchester City winger.
He was aided from the pitch before being replaced by Matthias Ginter.
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