Enrique was replaced by Suso for the final 20 minutes of the 3-0 victory at Loftus Road on what was otherwise a very satisfactory occasion for the Reds.
Assistant manager Colin Pascoe was asked about the extent of Enrique's injury and he said: "Unfortunately it looks like he's got a tear in his hamstring.
"He was terrific today, absolutely superb, and the way he's been performing these last couple of months has been a joy to watch.
"It's a shame, and hopefully he's not out for too long."
Spanish defender Enrique later said on Twitter: "Great win by the team today and thanks for all your support and messages for my injured leg. Hope to be back soon."