The 24-year-old was subbed out of Victoria's Sheffield Shield game after a volleyball hit him on the head during a warm-up on Saturday.
It was the latest frustrating and concerning head knock of Pucovski's frequently-interrupted but hugely promising career.
Victoria captain Peter Handscomb was left devastated for Pucovski, who was making his first-class comeback after suffering his previous concussion in October.
There were immediate calls in the media for him to retire, or take a long break from the game, after the incident at the Adelaide Oval, but Handscomb believes only Pucovski and doctors should decide that.
"I've texted him briefly, but trying not inundate him with messages - I'm sure he's had a lot over the last few days," Handscomb said.
"We've got to leave it up to people a lot smarter than me, I don't know much about the brain.
"First and foremost, we just want him to be healthy and happy.
"It was just a bit of a shock because he wasn't prepared for it, wasn't ready for it, so it's just knocked him around a little bit.
"As a group, we just want him to get better, whatever that takes, I don't know."
Pucovski scored an encouraging 54 in Victoria's first innings, opening the batting with Marcus Harris.
But he left the field after the first over of the final day, reporting concussion symptoms to team medical staff, and was replaced by Travis Dean.
Pucovski made his one Test appearance against India at the SCG in January 2021, scoring 62 but also suffering a shoulder injury in the field that required surgery and sidelined him for six months.
He suffered his first concussion when playing Australian Rules Football at school.
When fit and playing consistently, Pucovski would be a lock in Australia's Test team.
He has a first-class average of 53.42 from 25 matches with a top-score of 255 not out.
Cricket Victoria general manager Shaun Graf on Monday said Pucovski was determined to keep playing.
"He's realistic about it, but he's still very much in the corner that he wants to keep playing and we'll support that," Graf told SEN.
"However, if the medical advice is contrary to that, we need to have a very hard discussion."
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