Melbourne is forecast to endure a four-day spell of cold weather that hasn't been seen in the city since the year John Howard was sworn in as Australia's Prime Minister.

A mass of cold air passing over Victoria this week will keep Melbourne's maximum temperatures a few degrees below average for several days in a row.

In Melbourne, temperatures are only forecast to reach 11-12 degrees each day between Tuesday and Friday. This would be the city's first four day spell at or below 12 degrees since 1996.

Outside central Melbourne, temperatures could even get cold enough for snow to fall on some of the hills around the city. Snow is also likely in other low-lying parts of the state on Tuesday and Wednesday.

Temperatures will climb a little higher on the weekend as slightly warmer air returns to the state, with Melbourne forecast to reach 13-14 degrees on Saturday and Sunday.