The former Leeds and Levante full-back, 31, sustained a hand injury during the Cumbrians' 1-1 draw with Northampton on Saturday and tests later confirmed the problem was more serious than first thought.
"I went up for a challenge and I knew that I'd hurt my hand, but we found out afterwards that I had broken two bones in my hand," Harte told the club's official website.
"I see the doctor later today (Monday) and hopefully he will strap it up and tell me that it's fine for the weekend."
However, manager Greg Abbott remained cautious about the nature of the injury, and added: "It's that kind of injury where he might be fine for the weekend, or he could be ruled out for the rest of the season.
"We now have to keep our fingers crossed, which is something that Ian can't do at the moment, and wait to see what the medical people say."