The Collingwood premiership player, who moved home to Western Australia during the off-season, missed the first five rounds of 2013 with a right-ankle injury following a trampoline accident.
In just his third match for his new club, Wellingham was subbed out in the second term against North Melbourne on Friday night and has been diagnosed with a low-grade syndesmosis injury.
West Coast has the bye in round 12 which means Wellingham could possibly miss only four matches against GWS, Richmond, St Kilda, and Hawthorn if he recovers in five weeks.
There is more bad news for the Eagles with Will Schofield ruled out for three to four weeks with a compound dislocation of a finger on his right hand.
Schofield suffered the injury during the third term of Friday night's win at Patersons Stadium and bravely returned in the last quarter despite not being able to handle the ball.
Following surgery over the weekend, Schofield will be unavailable until after the bye.
There is some consolation for the Eagles with Andrew Embley compiling 28 touches and a goal on return for Swan Districts in the WAFL last Saturday after four weeks out with a foot injury.
Sam Butler will also be available after suffering a calf injury following the Eagles' loss to Port Adelaide in round five.