Motor vehicle premiums in Tasmania have been frozen for the third consecutive year as a result of low claims.

Tasmanian Infrastructure Minister Jim Cox says Tasmanians have access to "the cheapest car insurance in the country", following the Motor Accident Insurance Board's decision to keep premiums at their current level.

After two years of stable premiums, the board had the option to raise the rate 3.57%, or roughly $12 per car.

Mr Cox says the decision to keep premiums in check was made possible by lower than expected claims.