The 28-year-old suffered an impact injury while in training over the weekend, with a knee strike against his thigh causing a dead leg.
However, Boro boss Garry Monk confirmed that Gestede's leg start to bleed again after lengthy compression and ice treatment following the incident.
Monk told reporters on Thursday: "Rudy's is a bit of a freak injury really, he had a dead leg but it is quite rare for it to re-bleed after compression.
"He had a minor operation to relieve the bleeding so we don't know the extent or timeframe of the injury in terms of the time he will be out. We're hoping sooner rather than later."
Summer signing Martin Braithwaite is also expected to miss Boro's next game, the Championship trip to Bolton Wanderers this Saturday.