Monday's matches were delayed multiple times then ultimately abandoned in the afternoon amid heavy rain.
Rodionova, among a plethora of Australians involved in qualifying, was due to play the second match at Kia Arena on Monday, facing Frenchwoman Leolia Jeanjean, but will have to wait until Tuesday.
Australia's top-ranked woman was contentiously overlooked for a wildcard, despite impressive form, missing out on the final discretionary entry to Daria Saville.
Rodionova has moved up to a career-best No.105, but was No.112 at the time of the Open main-draw cut-off.
The 34-year-old dominated the lower-level ITF Tour in 2023, winning 78 matches on her way to seven titles as her ranking surged from No.302 to the brink of the top 100.
Rodionova carried that form into Brisbane - her first WTA event in nearly two years - where she beat recent top-20 talent Martina Trevisan and former Australian Open champion Sofia Kenin.
John Millman is hoping to qualify for one last Australian Open before his retirement. (Lukas Coch/AAP PHOTOS)
Retiring countryman John Millman was due to play on Tuesday, but will now play Italy's Alessandro Gianessi on Wednesday morning.
Millman also missed out on a wildcard and will have to take the long way through qualifying if he is to reach his final Open.
Tournament chief Craig Tiley backed the wildcard awarding process on Monday.
"There's lots of things that go into consideration: the age, the form coming in, how many matches they've played and what they've done over the last 12 months, who they compare to," he said.
"We are the grand slam of Asia Pacific.
"We also gave wildcards to a very exciting young player from China in Jerry Shang, who did a great job in Hong Kong, beating Francis Tiafoe.
"On the women's side, (we have) Mai Hontama from Japan, also young, a 24-year-old.
"Then of course we do an exchange with the US and the French (tennis bodies), and we've got some young players.
"Jason Kubler - he was just out (of) getting in direct, so we needed to help him get a wildcard.
"It was great to see James McCabe have an opportunity.
"All those players had an opportunity at some point in their careers and we've got to give obviously an opportunity for some young players to get that same opportunity."
26°C