McDonald-Tipungwuti, who spent six months in retirement last year, made his comeback as the Bombers' substitute in last Sunday's thrashing of Hawthorn.
The cult figure delighted fans with a final-quarter goal but reported soreness in the aftermath.
He will be monitored ahead of Sunday's clash with Gold Coast at Marvel Stadium.
"He pulled up sore from his first game back in a long time," Essendon high-performance manager Daniel McPherson said.
"We'll monitor his progress over the next couple of days and we'll have more info later in the week to make a call."
Former Melbourne tall forward Weideman is nursing a toe injury after kicking two goals on his Bombers debut against the Hawks.
"He kicked the ground and pulled up with a bit of a sore toe, but we're hopeful he'll be right for Sunday," McPherson said.
"He'll be on a modified program during the week and hopefully by Friday he'll be back up and running."
Stringer missed round one after sustaining a hamstring injury during the pre-season but is set to play against Gold Coast.
The explosive 28-year-old will be a valuable addition to a Bombers forward line operating without last year's best-and-fairest winner and leading goal-kicker Peter Wright (shoulder).
"Jake's progressed through all his training, he's ticked off all he needs to do," McPherson said.
"From a high-performance perspective, he's good to go and will be available for selection this weekend."
Wright, whose new four-year contract was announced just hours before he dislocated his shoulder, underwent successful surgery on Monday.
"He'll be in a sling for the next two weeks and then we'll be able to commence his rehab program after that," McPherson said.
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