An unhinged man randomly attacked two young girls who were riding the subway with their family in Brooklyn late Tuesday, police said.

The girls, 6 and 9, were on board a southbound B or Q train approaching the 7th Avenue station in Park Slope around 9:20 p.m. when a man wearing dark clothing and pushing a shopping cart approached them, cops said.

Without any provocation, the man started “acting irrationally” and yelling before kicking both sisters in the head, cops and sources said.

The girls – who had boarded the train a stop earlier with their mother and 6-year-old brother – complained of head pain and were taken to Brooklyn Methodist Hospital in stable condition, police said.

Their mother and brother were not hurt.

The crazed attacker left the subway station with his cart and had not been caught as of Wednesday morning, cops said.