The strike on the small clinic for communicable diseases occurred between 8:00 and 8:30 am (0600-0630 GMT), a local told an AFP correspondent among a group of foreign journalists on a guided tour of the town.
The journalists saw a completely destroyed building with a crescent sign at its entrance and ground scattered with gloves, oxygen bottles, pharmaceuticals and stretchers, but no victims.
Five ambulances were on standby as rescue teams scoured the rubble for other possible victims.
The foreign reporters were also taken to another part of Zliten where they were shown three damaged food storage buildings and another still on fire, which the government minders also blamed on NATO attacks.
Strewn around the site were hundreds of bags of rice, tomatoes and vegetable oil which smouldered with smoke, as firefighters tried to extinguish the flames.
Residents said the strike occurred at around 3:00 am (0100 GMT).
In the same compound, journalists also saw another completely destroyed building which bore the name "Agricultural Security".
The government minders also told the correspondents of other air strikes in the early hours of Monday that caused "civilian casualties," although they did not elaborate.
Zliten lies about 150 kilometres (100 miles) east of Tripoli, Gaddafi's stronghold, and 60 kilometres (35 miles) from the rebel-held western coastal enclave of Misrata, Libya's third city.