The petition has received nearly 15,000 signatures.
COTU has threatened to take legal action before in a similar scenario.
The plan could see crackdowns on motorists on the busy highways.
Raila made the sentiments moments after a consultative meeting with Kenyans.
Muhoozi has been a controversial figure and has once stated Uganda could capture Nairobi in less than two weeks.
Mudavadi's sentiments come as the U.S. is set to freeze aid to several nations.
The suspension comes just under a month since Ruto introduced it.
The deal was negotiated after President Ruto cancelled a deal with the Adani Group.
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Ruto made the sentiments at a rally in Taita Taveta County.