The 31-year-old will miss three to four weeks with the strained calf he sustained in the opening stages of Collingwood's 21-point win over Richmond on Saturday night.
Click here to view an updated injury list.
It was his first AFL game for the year after a pre-season hampered by a foot injury.
The club's director of football, Geoff Walsh, said that given Tarrant's summer struggles, it could take him until mid-season to really get going.
"He's had an interrupted last couple of months, so that's a possibility," Walsh said.
Walsh said captain Nick Maxwell was "fit and available" for Collingwood's Friday night's clash with Carlton.
Sharrod Wellingham is also available after serving his club imposed two-match ban for drinking while injured and missing a rehab session.
Wellingham was withdrawn from the VFL match on Saturday as a precaution, given the six-day break ahead of Friday night's clash.
Alan Didak is expected to play in the VFL this weekend while veteran Ben Johnson is available for senior selection after two games for Collingwood's the VFL team.
Travis Cloke, Heath Shaw and Chris Dawes ran laps on Tuesday at training while Johnson, Wellingham, Maxwell and Didak took part in the full session.
Walsh said Didak could require a few games in the VFL before he came into the seniors given his restricted pre-season because of an adductor injury.
"Alan is someone who generally finds touch pretty quickly," he said. "Having said that, he'll obviously need match conditioning because the tempo at VFL level is a fair way off AFL so you'd want to see him play at least a couple, I'd think."
Cloke's shoulder was treated in the second quarter against Richmond, but Walsh said he would be fine for the Carlton clash.
Dayne Beams trained on Tuesday after pulling up well from his first AFL game for the season, while Nathan Brown moved well following his VFL return.
Defender Alan Toovey said the Magpies were anticipating a big night out against the undefeated Blues.
"Carlton has played really well the last couple of weeks, and last week was a big improvement for us as well," he said.
"It's going to be a really good game to see where we're at with Carlton and the rest of the teams.
"Pre-season form, they didn't show much but as soon as the season proper started, they've really come out the last two games and played well.
"There's lots of areas in their game they've improved on, and our coaches have been studying that up and we're preparing for that now."
Walsh said ruckman Cameron Wood would be considered for a call up given excellent recent form and the Blues' use of two rucks, Matthew Kreuzer and Shaun Hampson.
