Professional glaziers were on the scene cleaning still this afternoon.
Reeves said that Peter seemingly managed to escape the incident unscathed, but more inquiries will be made to ensure this is the case.
He also said that they were unsure why the glass shattered.
Peter was the first T-rex skeleton to be displayed in the southern hemisphere.
T-rex skeletons are worth tens of millions of dollars, based on previous sales. In 2020, one sold for US$38.1 million (NZ$45m) at Christie's in New York.
The fossil was discovered in Wyoming, United States, in 2018 and is one of just 20 T-rex skeletons on exhibit in the world.
Peter is considered one of the most complete fossils of the iconic dinosaur ever found, at 47 per cent fossilised bone.