It will park at Heath Park School, enabling anyone aged 18 or over to get their first or second jab without an appointment.
Free vaccinations will be available on the bus, which will be in the car park of the Prestwood Road school, between 11am and 6pm both days, with Pfizer and AstraZeneca jabs on offer.
Councillor Jasbir Jaspal, the City of Wolverhampton Council’s cabinet member for public health and wellbeing, said: “Covid-19 infections are rising once again in Wolverhampton, so it's really important that people get both doses of the vaccination as soon as they can.
“People who have not had both of their Covid-19 jabs will not have the protection that the vaccine provides and be at greater risk of serious illness, hospitalisation or even death if they were to contract the virus.
“We’re taking the vaccine bus out and about into our communities to make it as easy as possible for people to get their vaccines and get protected.
“Apart from offering you protection against this deadly virus, another reason to get your jab is the change to the isolation rules which came into effect this week, which means that you no longer need to self-isolate if you are ‘pinged’ because you have been in close contact with someone with the virus, though you should still get yourself tested just to be safe.
“So, if you have not had your vaccination yet, or if it has been eight weeks or more since your first jab, please come along to the vaccine bus at Heath Park School, or call in to one of the other walk-in clinics across the city, and get your jab.”
In addition to the bus, walk-in vaccination clinics are being held daily at locations across the city, where anyone over the age of 18 can get a vaccination without needing an appointment.
Some locations are also offering vaccinations to 16 and 17-year-olds.
For full details, visit wolverhampton.gov.uk/localvaccine
Latest figures show there were 347.1 new cases of Covid-19 per 100,000 people in Wolverhampton over the last seven days.
That means 913 people tested positive for the virus in that same period – though the true number of new cases will likely be higher.