The on loan Preston star was replaced by Craig Wighton after just nine minutes in the 1-0 win with a thigh complaint following an innocuous incident on the edge of the Arbroath box.
The injury arrives after a positive start to Ginnelly's Hearts career.
With a goal against Dundee last week, the 23-year-old has made an impression on the club’s supporters with his pace and direct play, giving the team plenty of width which has been missing in recent seasons.
Ginnelly's qualities would be a huge weapon on the wide open expanses of Hampden Park.
Manager Robbie Neilson confirmed the the player is currently unlikely to feature on Hallowe’en against the club’s rivals, although tests will be undertaken.
“It’s a worry for next week,” he said. “It looks as though it’s his thigh so we will have a look at it. At this moment in time it probably look like he won’t make it.
“We were looking to get everyone through and everyone fit but that’s the way football is.
"We’ve had that lockdown and coming back into football there is going to be injuries. Everyone is the same so we just need to deal with it.”
Neilson was delighted with the three points, making it known how difficult a place Gayfield is to come.
Prior to the match, since the start of the 2018/19 season, the part-timers had lost just six times at home in the league.
“I thought it was going to be very, very hard," Neilson said. “We spoke about it all week, it’s one of the hardest places to come and get three points in Scotland when you look at stats, last two years they have been exceptional here.
"I thought we started the game really well then they came into it and made it really difficult. At the end of the season no one cares how you amass the points so it was about getting three points tonight.
“People think it’s Arbroath, you go there and you turn them over here, no one turns them over here. They are a good team, well organised and make it really difficult for you.
“All in all it’s a massive three points for us.”