More rain is expected to hit the region this week, with falls of up to 30 millimetres possible in parts.
The showers that arrived on Sunday are expected to clear by Tuesday, but Wednesday will see the rain return.
"Throughout Wednesday, we're going to see some tropical moisture coming down from the north, bringing rain and thunderstorm activity, firstly to the north of the state but then reaching southern parts at night," Bureau of Meteorology senior forecaster Michael Efron said.
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He said much of the state could expect rainfall of 15 to 30 millimetres, with quite unsettled conditions.
The rainfall was forecast to persist into Thursday as a low deepened across Victoria, Mr Efron said, with similar falls expected in the central districts.
He said some places in the north could see rain in excess of 50 millimetres.
Mr Efron said this was a classic weather system associated with La Nina, which the Bureau of Meteorology declared last week.
The rain is forecast to ease at the end of the week, delivering a mostly sunny weekend.
Daytime temperatures across the region are forecast to remain in the mid to high teens for most parts, up to the weekend.
A warning has been issued for sheep graziers in the North Central, Central and parts of the Northern Country districts, due to the rain and cold southerly winds.
Graziers are warned sheep and lambs exposed to these conditions could die.
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