Images posted on social media showed firefighters tackling the blaze on the top floors of a six-storey building known as The Cube on Bradshawgate at around 8.30pm on Friday night.
Greater Manchester Fire and Rescue Service (GMFRS) confirmed paramedics had treated two people at the scene, including one person rescued by crews via an aerial platform.
A spokesman said more than 40 fire engines were still at the scene on Saturday morning tackling "the last few fighting pockets of fire" in the building, which had been evacuated.
One eyewitness described the fire as "crawl[ing] up the cladding like it was nothing".
Ace Love, 35, told the PA news agency: "The fire kept getting more intense, climbing up and to the right because the wind was blowing so hard.
"We could see it bubbling from the outside and then being engulfed from the outside.
"A lot of students got out very fast, someone was very distressed, the rest were on phones calling for help.
"The fire got worse and worse, to the point where you could see through the beams, it was just bare frame."
University of Bolton student Shannon Parker, 22, lives in the building.
She told PA: "I was in my room whilst it was happening. I heard the fire alarm going off but it kept on going off so I just thought it was a drill at first until one of my flatmates shouted down the corridor that it was a real fire.
"So I ran out the flat as quickly as I could and I saw that it was one of the flats below mine and we went out by the fire exit."
She said she was being relocated to either a nearby hotel or another student accommodation building.
Authorities have asked anyone who was living at or visiting The Cube to register at the nearby Orlando Village student accommodation facility.
"We have divided the fire itself into four sectors of firefighting, allowing us to target our efforts on particular hotspots," GMFRS area manager Jim Hutton said in a statement.
"While the building does remain on fire, we are doing all we can to stay on top of this situation and soon extinguish the flames."
Road closures remain in place around the area.
Professor George E Holmes DL, President and Vice Chancellor of the University of Bolton, said: "Supporting the welfare of our students is our number one priority and we have moved swiftly to assist in any way we can.
"University colleagues have worked through the night to make sure support is in place for students over the weekend.
"We have assisted in ensuring students have been given temporary alternative accommodation at the Orlando student halls and in some Bolton hotels.
"We have also arranged to provide necessities such as toiletries for all students affected and are opening the University over the weekend so students can be supported. We will also provide food for them.
"I would like to stress that The Cube is not owned by the University of Bolton. It is owned and managed by a private landlord and the students were not on our premises when during this incident."
Secretary of State for Housing, Communities & Local Government, Robert Jenrick, tweeted to say officials were ready to offer assistance if required.
Incumbent Labour candidate for Bolton South East, Yasmin Qureshi, warned people to stay away from the area and said she would be in contact with the emergency services.
She said on Twitter: "There is an ongoing incident in Bolton town centre and the emergency services are asking people to stay away from the area for the time being. I will be liaising with the police and fire services to stay informed of developments."