Testing numbers fell again after just 16,932 were recorded on Sunday, and 17,102 on Saturday.
More than 50,000 tests were taken each day during the height of the state's latest lockdown.
Both of Monday's new positive cases were children, with one linked to a household cluster in Reservoir and the other was a close contact of the City of Melbourne case announced over the weekend.
The health department said no community exposure sites were associated with the two cases during their infectious period as both were isolating.
Health officials investigating an unlinked case announced Saturday have determined transmission likely occurred in a shared facility within a low-rise townhouse and apartment complex in Southbank.
The case that tested positive on Saturday lived in the same complex as an aged care worker at Arcare Maidstone who also tested positive.
Government nurses were on site on Monday working with residents to help them isolate and establish a pop-up testing facility.
The complex has not been listed as an exposure site but Victorians have been urged to check the state government's website for the full and frequently changing list.