The man went into Childsplay Nursery in Heathfield Road, Wavertree, shortly after 08:10 BST.
Police said he approached a man in the nursery before fleeing on a motorbike with a second man.
No-one is reported to have been injured and there was "no suggestion a firearm was discharged", Merseyside Police said.
Det Ch Insp John Webster said he believed what happened was "targeted" and the two wanted men had been "looking for a man who was in the nursery at the time who was not a member of staff".
He added: "I'm sure the vast majority of people in the community will be appalled to find that two men have walked into a nursery reportedly carrying a firearm when children and their parents were arriving at the start of the day".
Merseyside Police said officers remained at the nursery and a forensic examination was taking place.
Police are also making house-to-house inquiries and have appealed for witnesses or anyone with information to contact them.
Local councillor Andrew Makinson said: "In an area like this it's very unusual, and for it to happen in a nursery, it's utterly shocking for the local community.
"I'm sure the nursery will be reviewing its security, as will other nurseries across the city. There probably isn't a great deal they can do against these sorts of one-off incidents, but anything they can do, they will be looking at.
"It's the sort of thing that really does frighten people. It does cause a great deal of concern for people."
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