The small fire started about 11:45 a.m. Friday at Warrensville Center Road store, according to a police report.
The flames were quickly extinguished, and no one was hurt.
A surveillance video showed the woman standing near a children's pajama clearance rack, police said. The woman quickly walked away as the pajamas caught fire.
She then went to the front of the store and grabbed a blue bike.
She left the store with the bike when store employees were distracted by the fire.