On both days, Mr Andrews wore a mask as he was driven to parliament but took it off before he walked through the car park.
Victoria Police confirmed on Friday the Premier had been issued two $200 infringement notices over the incidents.
Currently, Melburnians aged over 12 must wear a fitted face mask whenever they leave their home, indoors or outdoors, unless a lawful exception applies, including for broadcasting purposes.
In a statement earlier on Friday, Mr Andrews apologised and said he would pay a fine if police issued one.
"If they do not issue a fine I will donate the same value to a charity working to support people in this pandemic because whilst this was an oversight, oversights matter - everyone needs to follow the rules and I am sorry it occurred," he said.
Treasurer Tim Pallas defended the premier, who he said has been "pretty diligent in terms of his behaviour" throughout the pandemic.
"I had a brief look at the footage and it looks like he is approaching a camera for the purpose of doing a piece to camera. You are allowed to not wear a mask for that and we will leave it at that," he told reporters at the daily COVID-19 briefing on Friday.
Opposition Leader Matthew Guy said most Victorians had "momentarily forgotten a mask" but noted Mr Andrews walked "some distance" without wearing his.
"He's done it in front of media, which is probably a bit silly but I will leave that to police," he said.