Street leads the Abbotsford Heat this season with 12 goals and 19 assists in 44 games. He signed with Calgary last summer as a free agent.
The Flames, meanwhile, have placed centre Mikael Backlund (MCL sprain) and goaltender Miikka Kiprusoff (MCL sprain) on injured reserve.
Kiprusoff was added to the IR retroactively and is considered day-to-day, while Backlund is expected to miss four to six weeks.
Flames also have activated defenceman Anton Babchuk while centre Michael Cammalleri remains day-to-day (hip flexor) and rookie Sven Baertschi remains week-to-week (hip flexor).
Calgary's next game is Saturday night in Vancouver against the Canucks.