First Bus West Yorkshire warned of severe delays of "up to 75" minutes, adding that cancellations were "unfortunately inevitable".
There was no information available as to the reason for the delays, although bus company Arriva said it was due to a "high volume of traffic" coming in and out of Leeds.
First Bus added there was congestion on Boar Lane which was having a knock-on effect to services across the Leeds network.
Metro Travel said: "Heavy congestion is reported across Leeds area including Leeds city centre.
"Reports of queuing traffic on York Street back to Infirmary Street."
Commuters in Leeds unveiled a campaign for publicly-funded electric bus services in the city earlier this month, as concerns grow around the volume of traffic, air quality and lack of transport infrastructure.
Leeds is one of Europe's biggest cities without its own metropolitan transport service such as trams or metro rail.