"He has a whole string of convictions and just two weeks ago he was convicted of a number of charges again, sentenced to three years jail, two on another, with five years probation and a suspended sentence," Andrews said.
"He has been denied entry into the United Kingdom because he was caught with others causing affray at Heathrow Airport," the minister told Australian radio.
"He doesn't seem the sort of bloke we want in this country."
Andrews said Snoop's reputed gang ties were also taken into consideration.
"This man has been a member of a Los Angeles gang - and is still associated with it apparently - that's been involved in murder, robberies and drug dealing in the LA area," he said.