The suspects climbed over a fence to access the velociraptors, which were part of an outdoor display.
They then beheaded the fibreglass dinosaurs with a handheld grinder or hacksaw, said local police.
Authorities are appealing for information on the vandals, whom they have branded "idiots".
Police spokesman Rod Anderson told the Australian Broadcasting Corporation that the theft was "a pretty stupid act", and that the perpetrators may have wanted to keep the heads as trophies.
"We're expecting these perpetrators, because they're obviously not very smart, will tell people about it... We want people to give us information identifying who these idiots are," he was quoted as saying.
The incident took place at the National Museum of Dinosaurs on Saturday night and was only reportedly discovered the next morning by visitors.
Museum supervisor Mitchell Seymour told The Canberra Times that children "had been asking their parents: 'Mum and Dad, what's happened to the dinosaurs?'".
The museum appears to be a frequent target. In March 2013, a dinosaur was stolen in an apparent birthday prank and found in a local man's home.
Months later three other dinosaurs were found vandalised at the museum. The next year, another dinosaur was stolen and later found damaged in a nearby park.

Rothamsted said that crops had been vandalised, causing "significant" damage.
The incident took place on Sunday morning at the centre's test site in Harpenden, Hertfordshire.
The project aims to see whether the modified crops can deter aphids - a major wheat pest.
Rothamsted has previously pleaded with anti-GM campaigners not to destroy their experimental plots, which they say could help reduce pesticide use.
But opponents of GM technology claim that planting the crops in the open air would allow modified pollen to get out into the surrounding environment.
After the break-in at the site, Rothamsted scientist Toby Bruce  
          wrote on Twitter
 that wheat seeds appeared to have been strewn onto plots, and the tops of plants had been cut off.
However, the laboratory said the account was anecdotal and might not be accurate. In a statement, Rothamsted commented: "The intruder caused significant, random property damage, but failed to disrupt the experiment in this attack."
The lab's director Prof Maurice Moloney said the act was an attempt to "deny us all the opportunity to gather knowledge and evidence" on a possible new approach for reducing the use of pesticides.
A 50-year-old man from Devon is to appear at the Central Magistrates Court in St Albans on 13 July.
The crop being trialled at Rothamsted contains genes synthesised in the laboratory. It will produce a pheromone called E-beta-farnesene that is normally emitted by aphids when they are threatened by something.
When aphids smell it, they fly away.
Anti-GM group Take the Flour Back has vowed to "decontaminate" the site unless the research is halted.
The event was trailed on the organisation's website as "a nice day out in the country, with picnics, music... and a decontamination".
There is no suggestion the man who has been charged is linked to Take the Flour Back.
Eleanor Baylis, from the anti-GM group, said in a statement: "We have no information about this incident, but are relieved if the quantity of GM pollen released from the trial has been reduced.
"The British people are clear that they're not swallowing this technology."
The protesters have previously declined an invitation from Rothamsted to meet scientists behind the project and, following a heated debate on the BBC's Newsnight programme, a planned day of action on 27 May will go ahead.
But a spokeswoman for Take the Flour Back told BBC News the group would be interested in engaging in a public debate with wide participation. She said the decision not to take part in the debate proposed by Rothamsted was due to the specific conditions of the event.
Paul.Rincon-INTERNET@bbc.co.uk
Australian police are on the hunt for vandals who hacked off and stole the heads of three dinosaur statues from a Canberra museum.
[NEXT_CONCEPT]
A man has been charged with criminal damage following a break-in at the Rothamsted Research centre where a trial of GM wheat is being held.