Rabbi Stern, from New York, has already appealed twice to the beard ban without success but has vowed never to shave his beard off.
The army has previously allowed three Sikh soldiers to keep their turbans and beards despite its policy, while in 1976 a rabbi won a similar case against the US Air Force.
Rabbi Stern said: "By not trimming my beard, I represent the unadulterated view of the holy Torah, the way we believe a person should live.
“I believe this is my calling and mission. I won't give up this fight."
The army is required to respond to the lawsuit within 60 days.