Governor Frances Adamson, Labor Leader Peter Malinauskas and his deputy Susan Close have all been forced into quarantine after being identified as close contacts of a confirmed case.
They have all tested negative, but under current rules must isolate for seven days.
Because of the virus scare, Health SA initially advised the parliament it should not sit.
But Deputy Premier Dan van Holst Pellekaan told the house on Thursday morning that revised advice indicated it could resume.
Among the state's 47 MPs, only the deputy premier, leader of opposition business Tom Koutsantonis and independent MP Frances Bedford were in the chamber for the brief session.
"In the last short while advice has been received saying that parliament can now sit," Mr van Holst Pellekaan said.
"But because many MPs would not be available to sit right now because they were following the first set of health advice, I am reliably informed that it will not be possible for the house to make up a quorum at this point in time."
Speaker Dan Cregan ruled the house would reconvene at 2pm.
Earlier Government House confirmed Ms Adamson had been identified as a close contact of a coronavirus infection.
"Her excellency was tested at about midnight and has returned a negative result," it said in a statement.
"As a close contact, she will nonetheless isolate within Government House for as long as advised by SA Health."
Lieutenant-Governor Brenda Wilson will be appointed administrator of the state during the governor's isolation.
Mr Malinauskas and Ms Close have also confirmed their negative tests after having contact with former SA premier Jay Weatherill who has tested positive.
Mr Weatherill, who now lives in Perth, attended a school reunion last weekend which has sparked other infections including SA's first cases of community transmission since the state reopened its borders last week.
SA Health reported on Wednesday two men in their 50s had tested positive for the virus after attending the same event as some interstate travellers.
A number of exposure sites linked to the two cases included a theatre venue in suburban Norwood, a seafood restaurant, a cafe in Adelaide's CBD and the Business SA headquarters in Unley.
Under current arrangements, SA is open to vaccinated travellers from all states and territories, with some requirements for testing and quarantine.
International arrivals are required to quarantine for 14 days, regardless of where they come from.
Local restrictions, such as mandatory mask-wearing on public transport and in most venues, also remain.
The state's transition committee met on Tuesday but left all travel and local restrictions unchanged despite concerns over the new Omicron variant of the virus.
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