Reyna, 17, was named in Dortmund's line-up as the Bundesliga returned from a two-month suspension due to the coronavirus pandemic but sustained an injury in the warm-up. He was replaced by Thorgan Hazard.
Hazard teed up the opener for Erling Haaland and scored one himself in between a double for Raphael Guerreiro, helping BVB cruise to three points at an empty Signal Iduna Park.
Schalke lost Jean-Clair Todibo to a muscular injury at half-time, while Hazard hobbled off when he was replaced by Jadon Sancho in the 79th minute.
Favre insisted the Belgium international was only struggling with cramp, but he expects a number of players will suffer from niggles as the Bundesliga gets back up and running.
"A lot of teams will have a few players who will be injured," said Favre. "We started very late with the 10 against 10 games, tackling and so on.
"I hope Reyna has nothing. It won't be long for [Axel] Witsel and [Emre] Can, [Dan-Axel] Zagadou won't play again this season.
"Marco Reus has not yet played with the team. Nico Schulz has injured himself again, he is not allowed to do anything for two to three weeks.
"Hazard only had cramp, no injury."
Dortmund players kept their distance when celebrating – a touch of elbows the most contact they made with one another – while substitutes were spaced out on the sideline and wore masks.
Favre acknowledged the atmosphere behind closed doors was unusual but was proud of the way his team performed.
He said: "4-0 against Schalke - that's quite okay. The key was that the team played well together, also defensively. That was very, very special.
"There wasn't any noise, you shoot at the goal, make a top pass, a goal - and nothing happens. That's very, very strange. We really miss our fans.
"It was a completely different game than usual. It's hard to judge how good the game was. I had the feeling that it wasn't as committed as planned. The players were very focused on their task."
An error from goalkeeper Markus Schubert preceded Guerreiro's opener, while Dortmund's last two goals came at the end of swift counter-attacks.
Schalke boss David Wagner said: "We didn't have a good game, and at really bad moments we conceded the goals. At least two goals would have been easy to defend.
"Derby defeats are unpleasant in principle, even in this bizarre atmosphere. The feeling of the second half of the season is not there yet. The situation is quite extraordinary.
"I don't think we had any major physical deficits. We had deficits in defending the right spaces."