A 44-year-old man has been charged after allegedly breaking several windows and two glass doors at Parliament House in Hobart on Saturday night.

Police were called about 11.20pm after 10 windows and two glass doors were damaged, including the front door to Parliament House.

No entry was gained to the building.

Police allege the Dover man was also involved in breaking 26 glass panels at the Wrest Point Convention and Entertainment Centre in the early hours of Monday morning, in the Hobart suburb of Sandy Bay.

"Significant repairs and replacement costs are expected in both incidents," Tasmania Police said in a statement.

"Following investigations, police obtained a warrant for the man's arrest.

"He was located and arrested in Hobart on Tuesday, 6 October, before being taken to Hobart Police Station."

The man was charged with offences relating to the destruction of property and will next appear in the Hobart Magistrates Court in January.

Repairs on the damaged windows at Parliament House began on Sunday morning.