Both women were taken to hospital where they were reported to be in stable condition.
Police said they were looking for a man who could be linked to the attack.
A tourist from Spain named Julia Garcia Valles, 24, was queuing up on West 53rd Street to enter the museum when people shouted "It's shooting!"
and began to rush out the doors in panic.
Some fell to the floor in confusion, Valles said.
- We were really scared, she added.
Alyssa Katz, deputy editor of the local news site The City, was on her way to meet friends at the museum when she saw people running out.
Katz, 53, said she spoke to two rescued French tourists who said they had seen someone stabbed in the forearm.