The examination of Viney's fourth metatarsal showed no fracture however and he will be confined to a moon boot for a couple of weeks before he returns to training.
Melbourne football manager Josh Mahoney said Viney would gradually build his training load once out of the moon boot.
"The good news is that there was no fracture in his toe so we got on to it early," Mahoney told AFL.com.au.
Viney's absence is a blow to the Demons who could have used his hardness inside the centre square to complement James Magner and Nathan Jones. He has played six games for the Demons in 2013.
The news was better for Melbourne's other talented youngster Jimmy Toumpas who was subbed off the ground with an injured ankle at half-time of Sunday's game against Richmond.
Mahoney said scans had cleared Toumpas of any major damage or a fracture but the 19-year-old remains an unlikely starter for this week's game against Fremantle in Perth.
"He still has swelling and a sprain so at this stage he looks unlikely for this week but we will monitor him throughout the week," Mahoney said. "He might come up but he looks unlikely."
Toumpas has played four games in his first year at Melbourne.
Recruit Shannon Byrnes, who missed Sunday's game with a wrist injury, will undergo a fitness test before being declared available to play against the Dockers.