Love underwent surgery last week after his left shoulder was dislocated when his arm was yanked from the socket by Boston center Kelly Olynyk in Cleveland's series-clinching win in the opening round.
The Cavs intended to hand out the slings, adorned with a sponsor's name, during their Eastern Conference semifinal series against Chicago but scrapped the idea.
A team spokesman would not comment on the giveaway. It's not known what the team plans to do with the unused slings.
The Cavs handed out small white towels for Tuesday's Game 2 against the Bulls. The team typically gives out T-shirts during the postseason.
Olynyk will serve a one-game suspension for his actions against Love.