The 35-year-old Gonchar was hurt in Tuesday's 5-1 win over St. Louis when he landed awkwardly following a collision with St. Louis forward David Backes late in the second period.
"Surgery was not a consideration at all," Coach Dan Bylsma said Wednesday on the team's Web site. "(The bone is) not displaced. It's a small fracture (and) will heal on its own."
Gonchar, a 14-year NHL veteran and a key cog in Pittsburgh's defense, has compiled eight points (two goals, six assists) while leading the reigning Stanley Cup champion Penguins to an 8-1 start in the 2009-10 season.
He is in the final season of a five-year, $25 million contract.
Gonchar missed most of last season with a shoulder injury he suffered in an exhibition game.
It later required surgery.