Smith was joined by defender Ryan Gardner in suffering a setback from the hitout in Ballarat, with the latter already confirmed to miss Round 1 due to an elbow injury.
The club confirmed on Wednesday that Smith has sustained a footy injury, with a plantar fascia ailment potentially ruling the 26-year-old out for an extended period if surgery is required.
The news isn't all bad on the injury front for the Bulldogs, with Cody Weightman (adductor) and Jason Johannisen (calf) in the mix to face North Melbourne at Ikon Park on Saturday for the Dogs' one and only pre-season match.
Young defender Jedd Busslinger, who made the move east from WA as the 13th overall pick in last year's National Draft, is building his workload after requiring surgery last year following a shoulder issue sustained in July.
The key defender is in line to play VFL football in the opening rounds of the season, commencing later this month.
A brief statement provided by the club this week revealed Tarrant will be sidelined for the short term.
Midfielder Marlion Pickett is battling an adductor issue that will see the Western Australian sidelined for the coming week, with the premiership Tiger potentially playing for Richmond's VFL side for their pre-season match next weekend.
Richmond will face Melbourne at Casey Fields on Saturday before they plan for their Round 1 bout against Carlton at the MCG in two weeks' time.