Gomez shifted across to right-back with Joel Matip partnering van Dijk in the centre of defence and the youngster impressed in the early stages.
However, he was on the receiving end of a challenge from Burnley defender Ben Mee as he chased down a ball towards the touch-line, resulting in him crashing in to the advertisement hoardings.
Speaking to reporters, Klopp suggested that Gomez's injury could be far from innocuous and revealed he had previously asked referee Stuart Attwell to protect his players from dangerous tackles.
Klopp confirms that Gomez has an ankle injury and is facing a spell out #LFC
“Joe is injured and probably not only a little bit. We have to see tomorrow. It's [his] ankle, yes,” he said.
“After the first challenge, a sliding tackle from seven or eight yards, I said to the ref: ‘Please tell them you can't do that'. Someone has to say ‘stop doing that'.”
Gomez will undergo a scan on Thursday to show the true extent of the injury, however the initial update from the boss is worrying to say the least.
The 21-year-old has looked accomplished partnering van Dijk in defence this season, with his impressive form one of the major positives so far.
The worry will be if Gomez has suffered a high ankle sprain, an injury that may mean corrective surgery that keeps athletes out of action for up to a year. However, the hope will be that it is just a minor sprain.
Gomez would be a big miss for Klopp in central defence during this busy festive period, with Joel Matip and Dejan Lovren the other possibilities.