Mr Andrews took to social media today to share the latest update on his recovery.
He did however flag he would not be back to his usual duties this month.
“My physio is also going well, but it’s clear I won’t be able to return to work before the State Budget in May,” he said in the post.
“The good news is my team of specialists are confident that I will be back in June.”
Mr Andrews suffered broken ribs and spinal damage after falling on wet stairs while staying at a holiday home on the Mornington Peninsula on March 9.
He was released from hospital on March 15, about a week after he fell.
“A CT scan has revealed several broken ribs and vertebrae damage, and subsequent medical advice has recommended I remain in intensive care for the next few days,” he said in the statement.
Today, Mr Andrews thanked his team and medical professionals.
“You only get one chance to properly recover from serious injuries and while it’s frustrating to be away from work, there is no alternative,” he wrote on social media.
“I want to thank (Education minister) James Merlino and all the team who are working so hard and doing so well.
“And, of course another big thank you to the health professionals who are looking after me. Above all, thanks to all those Victorians who have sent messages of love and support – it means a lot.”
Mr Merlino stepped in as acting premier when Mr Andrews was injured.