At the conclusion of the UFC 175 broadcast, Ronda Rousey was shown backstage with stitches in her hand. The stitches seemed to go across the knuckle at the joint of her right index finger and her hand.
The injury to her hand likely eliminates any further need to speculate on her availability to save the UFC 176 card. Joe Rogan had asked Rousey "at the request of the production truck" if she would be willing to take a fight on roughly one month notice and save the event, which lost its main event due to a Jose Aldo injury.
Rousey, who defeated Alexis Davis in sixteen seconds on the card, suggested that she might be willing, but was non-committal, referencing a scheduled knee surgery and stating that she needed to talk to her team.
Dana White seemed upset that Rousey was asked and appeared to apologize to Rousey in the cage, appearing to say (per my amateur lip reading skills), "that's not going to happen."
White also tweeted after the fight took place, "Ronda may have broken her hand in that fight."
While we don't know if there was a break, there appears to definitely have been an injury, and that's likely more than enough to prevent any sort of quick turnaround.