The winger had put the visitors into a 1-0 lead at Carrow Road on Sunday, but his participation in the match was curtailed when he was carried off the pitch following an innocuous challenge with Sebastien Bassong, with the 26-year-old taken to hospital for scans on a suspected fractured ankle.
That led to six minutes of first-half injury time and Norwich took full advantage as Gary Hooper's stunning volley secured a point for Chris Hughton's side.
The draw means Swansea have won just once in their last six matches in all competitions, but Laudrup said Dyer's injury is a more pressing concern.
"The health of a person is the most important thing. We know football can have injuries. Hopefully I'm wrong, but this looked much more serious," he said.
"We have to wait a couple of days for an X-ray and a scan, and we all cross our fingers to hope it is not that bad. That will overshadow everything else. It is just a game of football."
Laudrup felt his charges had controlled proceedings at Carrow Road until Dyer's injury, but the Dane was happy to reach the 20-point mark as a result of the draw.
He added: "That game of football we controlled quite well in the first half and then just before half-time, after the injury, we had 10 minutes where we lost a little bit of perspective and they scored a fantastic equaliser.
"We have reached 20 points after 16 games. That is positive after a very difficult week for us."
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