The deaths were ruled homicides, but authorities didn't disclose how the victims were killed.
Panus said money was taken from the business, but wouldn't say how much. Police had no suspects by late Monday afternoon.
Police said the victims were waitress Tammy Cantrell, 44, and cook Mark Gerstner, 24. Employees, customers and others gathered outside the restaurant, some sharing hugs, during the day as investigators worked. Employees at the scene declined to comment.
The Steak'n Shake is on a busy commercial thoroughfare in the small community of Green Park, about 10 miles outside St. Louis city limits.
An executive said the Indianapolis-based chain would do everything possible to help their families. "Our hearts go out to the families of the associates who were killed in this senseless act of violence," Sardar Biglari, chairman and chief executive officer, said in a statement.
The restaurant ordinarily is open 24 hours but closed for a few hours early Monday for routine pest extermination. Panus said investigators believe the robbery and homicides occurred sometime between 2:30 a.m. and 4:30 a.m.
Investigators were checking if any surrounding businesses had captured activity on surveillance tapes. Panus wouldn't say whether the restaurant had surveillance cameras.