The highly-rated Manchester City left-back has joined the Jambos on a 12-month loan deal.
But he lasted just 27 minutes as a half-time substitute during Wednesday’s warm-up clash with Irish side St Patrick’s Athletic before pulling up.
Cathro, however, says the decision to replace the 21-year-old with Angus Beith was purely precautionary.
He told the Hearts website: “He just felt something when he turned and this is a point in the season where you just don’t need to take any risks.
“We’ll just manage that and make sure it’s okay.
“Pre-season is about building our conditioning and also about trying to avoid injury as best we can.”
The Jambos suffered a frustrating 1-0 loss to their part-time opponents but there were positives as Smith-Brown’s fellow new signing Kyle Lafferty also made his first appearance in a maroon jersey shirt after being introduced with quarter of an hour left.
And Cathro revealed he will treat the Northern Irishman - who has started just 22 club games in the last three seasons - with kid gloves as he looks to build up his fitness.
“It was important that Kyle got minutes,” he said. “He’s not had anywhere near as many training sessions as everyone else so we’re just going gradually with that.
“But it was good for him to get onto the pitch and we’ll go step by step to build him up.
“It was a really worthwhile workout. We got our conditioning up and put in a lot of running, which we wanted to do.
“We played against a team that’s pretty much in the full flow of their season so it’s a really good match, I’m really pleased with the game as an exercise for us. So it’s been positive.”