The arrests on Sunday came amid fresh demonstrations in Sudan's capital Khartoum and other cities in response to a call by a coalition of professional unions to push for Bashir to step down.
Witnesses told the Reuters news agency that security forces blocked professors and lecturers from coming out to protest outside the university, arresting at least eight.
It was the first time the faculty of the country's oldest and most prestigious educational institution joined the protests since they began last month.
The rest were forced to return into the faculty clubhouse, where security forces surrounded the building trapping about 100 professors and lecturers inside for nearly three hours.
"We demand the president of the republic to step down," one placard read carried by the lecturers inside the clubhouse, according to pictures posted on social media.
A police spokesman could not immediately be reached for comment.
Intermittent protests have rocked Sudan since anger over food shortages and rising bread prices erupted into demonstrations in the city of Atbara in the north on December 19.
Security forces have used tear gas on occasions, live ammunition against demonstrators and rounded up more than 2,000 people.
The Sudanese government has said that 19 people were killed in the protests, including at two members of the security forces. Amnesty International has put the death toll at 37.
'Peace, Justice, Freedom'
In Sunday's protests, witnesses said hundreds of men and women marched from three separate locations in the capital trying to reach the presidential palace in central Khartoum but were dispersed by security forces using tear gas and stun grenades.
"Police are not even allowing 10 people to gather," a witness told AFP.
Video footage posted on social media networks showed protesters fleeing down streets and alleyways in the downtown area trying to escape the noxious gas.
A separate protest in Wad Madani, Sudan's second largest city, where demonstrators chanted for "peace, justice, freedom", was also dispersed by security forces using tear gas, according to witnesses.
In the northern town of Atbara, the local market was shut down as protesters took to the streets.
The protests were smaller than previous demonstrations.
As protesters attempted the march on Sunday, Sudan's Labour Minister Bahar Idris announced that a pro-government rally would be held on Wednesday at Khartoum's Green Yard, a large open ground in the capital.
The rally would express "the choice of the Sudanese people and address the present crisis", Idris, a former rebel from war-torn Darfur, told reporters at a press conference.
Wednesday's rally would be the first pro-Bashir demonstration since anti-government protests erupted last month.
The president, who came to power after a 1989 coup, has sought to defuse the anger sweeping the country by pledging to do more for the poor. In an address to the nation on December 31, Bashir said he would maintain state subsidies on commodities, raise wages and refrain from introducing new taxes.
He has since ordered an investigation into the violence during the anti-government protests, and on Saturday, sacked the health minister.
The country has been facing a mounting economic crisis over the past year led by an acute shortage of foreign currency.
The cost of some commodities, including medicines, has more than doubled and inflation has hit 70 percent.
Food and fuel shortages have been regularly reported across several cities, including Khartoum.