He batted sixth against left-hander Randy Wolf.
Pena suffered the injury during Monday's 4-1 victory over the Arizona Diamondbacks.
The Cubs also placed Andrew Cashner and Randy Wells on the 15-day disabled list and recalled pitcher Jeff Stevens from Triple-A Iowa. Pitcher Casey Coleman is expected to be activated in time for Sunday's start.
Bruce Levine covers baseball for ESPNChicago.com and ESPN 1000.