Max Fineday says the situation could become "chaotic" if the issue isn't resolved before winter arrives.
He says with no transit, some students on the opposite side of the city haven't been able to get to their classes.
He also says students are having to spend money on temporary parking passes after already paying a mandatory $76 fee for a pass which allows students to ride the bus to school.
Fineday says the students union has decided to withhold 60 cents a day from the money usually paid to the city for the transit passes for each of the more than 14,000 students.
He says it's "ridiculous" for students to have to pay for a pass when they aren't able to use buses.
The City of Saskatoon says it will be providing refunds for all transit pass holders, and says more information will be released early next week.
About 330 transit employees were locked out on the weekend after serving strike notice, bringing regular transit services in the city to a halt.
The union wants a 22.25 per cent wage increase over five years to bring its members up to average levels for other transit workers in Western Canada, while the city had countered with an offer of 10 per cent over four years.