The Swansea left-back missed seven months of last term due to a broken ankle and admits he initially feared the worst for his team-mate.
Dyer was stretchered off during their 1-1 draw with Norwich at the weekend when he landed awkwardly after an aerial challenge with Sebastien Bassong.
The club revealed on Monday he suffered ligament damage and they are now assessing how long he will be out for.
Dyer has been a standout player for Swansea recently and Taylor hopes he will make a speedy recovery.
He told Wales Online: "It's not great when things like that happen.
"Even though we weren't sure of the diagnosis it looked like it really was a bad one.
"He has been in great form and the side will miss him but how he is playing really doesn't matter when things like that happen because your first thoughts are with him and how it could happen to anyone - as I know myself.
"I certainly didn't enjoy it happening to someone else and it is in those moments that your thoughts on the game go out the window and it was great to hear it is not as bad as first feared or as everyone thought.
"It could have easily been a lot worse so we are thankful for that."
Losing a key player coming into an important period of the season isn't ideal, but Taylor thinks the Swans have enough about them to maintain their top-half position.
He continued: "There are some tough games coming up, we know that.
"We are about three games away from the halfway mark and 20 points is a good total to have right now even though many people feel that we haven't really got into top gear yet.
"The next three games are tough - when I saw Everton at Arsenal they looked like one of the best teams in the league but we're looking forward to it."