Both players were hurt late in the third quarter of Thursday night's 24-21 win at Arizona.
Tonyan's was a non-contact injury that occurred at the end of a 33-yard completion that helped lead to a touchdown. The catch had given Tonyan seven receptions for 112 yards with a TD over his last two contests.
It was a sign his production was returning to 2020 levels after a relatively quiet first six weeks of the season, though his value to the offense as a blocker and in other roles had continued to grow to an immeasurable level.
"It's sickening for me as a coach," LaFleur said. "Bobby is a tough one to replace. He's a guy that's so versatile in terms of both the run game and the pass game."
He indicated the coaches would take a "by-committee" approach to make up for Tonyan's absence and perhaps shift some personnel groups around. The depth at tight end that includes veteran leader Marcedes Lewis and developing prospects Josiah Deguara, Dominique Dafney and Tyler Davis, plus converted defensive lineman Bronson Kaufusi on the practice squad.
Hill was injured returning a kickoff on a violent collision with Arizona's Jonathan Ward, who was also hurt on the play. Receiver Malik Taylor replaced Hill as the kickoff returner, and LaFleur said the coaches would explore other potential options as well.
Defensive lineman Kingsley Keke also left Thursday night's game with a concussion, his second within the last calendar year.
The latest injury news aside, the Packers are hoping the long weekend and extra time before their Week 9 trip to Kansas City will allow the team as a whole to get healthier.
Green Bay played Arizona without receivers Davante Adams and Allen Lazard, who were both placed on the COVID-19/reserve list this past week. Fellow receiver Marquez Valdes-Scantling also missed his fifth straight game with a hamstring injury and remains on injured reserve.
Any of them could be back soon on offense, along with All-Pro left tackle David Bakhtiari, who returned to practice two weeks ago for the first time since last December but has not yet been activated from the physically unable to perform list. LaFleur considers Bakhtiari's situation "day to day" at this point in terms of when he could get the green light to play.
Rookie center Josh Myers has been out with a knee injury since the opening series three games ago and is on IR, with no indication his return is imminent, though the last update was he's not done for the year.
On defense, LaFleur indicated cornerback Kevin King is close to returning after missing the last three games with a shoulder injury.
There also remains hope the defense's two second-team All-Pro players, edge rusher Za'Darius Smith and cornerback Jaire Alexander, could return this season, though there's no new update or specific timeline.
Smith hasn't played since Week 1 because of back surgery, while Alexander has missed the last four games due to a shoulder injury he's trying to let heal without surgery.
"I think everybody is totally invested in the process and trying to come back for this football team because we're going to need everybody," LaFleur said. "We've fought through a lot of adversity in terms of the injury bug this year.
"We've found different ways to win, which is always good. But certainly, we're looking forward to getting some of these guys back."