The warrants say it happened between February 1 and the end of March at an apartment in the 900-block of South East Street.
Gerald Thomas Swinehart, 26, and Marlaine Victoria Coffey, 28, are charged with intentional felony child abuse causing serious physical injury.
The warrants state that strapping the child to the gate caused "bruising to her wrists and ankles."
Swinehart is also accused of "pushing/kicking the victim down which caused the victim's lower teeth to intrude through her bottom lip."
Bond for Coffey was set at $50,000. Bond for Swinehart was set at $100,000.