A similar incident happened last week in Inchicore.
As a result, the Dublin Cycling Campaign has warned about the dangers of pedalling across Luas tracks.
Rubber inserts into tracks would ensure wheels could not get stuck, spokesman Dr Mike McKillen saaid.
The mechanism allows trams to travel along the lines but stops bicycle wheels getting trapped.
"We have asked for the Railway Procurement Agency to use the insert," Mr McKillen revealed.
"It's a major issue and the RPA knows it's a major issue."
Both the RPA and tram operators Veolia should upload a video on to their websites showing cyclists exactly how they should cross a tram track, he added.
The most important thing is to cross at a right angle, otherwise the wheel is at risk of getting stuck.
Veolia does not have figures on the number of cyclists who fall off their bikes on Luas tracks as it is only reported when the service is delayed.
A spokeswoman said "the jury is still out" on rubber inserts as the material degrades.