The attack took place near Glasgow's city centre
The Sudanese men were attacked by a gang of about 10 youths, some aged as young as 13, on Wednesday night.
One of the asylum seekers needed hospital treatment after he was hit with a bottle.
Strathclyde Police are treating the attack, which took place in St Mungo Avenue, as a racist incident.
It has also been condemned by both Glasgow City Council and the Scottish Refugee Council (SRC).
Strathclyde Police said two of the victims, aged 30 and 27, were repeatedly punched and kicked and received cuts to their body.
The 30-year-old was also struck in the face with a bottle by a member of the gang, while the third man was uninjured.
A police spokeswoman said the victims had already provided descriptions of two of the attackers.
Another is believed to be aged between 17 and 18, more than 6ft tall, with dark hair and wearing white sports clothing.
A council spokesman said: "This is dreadful news following on from the other attacks against asylum seekers in the city.
"The council and its partners, including the police and the Scottish Refugee Council, met yesterday to decide what to do about this problem.
"We have pledged to make every effort possible to tackle this racism and to make Glasgow a safe place for asylum seekers."
An SRC spokeswoman said: "This confirms the urgent need within the city to support asylum seekers and fight racism.
"We call on all in society to show the utter contempt with which they view
such behaviour and attitudes.
"It is scandalous that people's lives are being threatened in Glasgow, when they have come here for safety."
Strathclyde Police said on Wednesday that it was launching special patrols in an attempt to stamp out abuse aimed at asylum seekers in the city.
The initiative was prompted by growing concern at the number of apparently racist attacks on asylum seekers.
Two Palestinian brothers were attacked last month, while an Iraqi Kurd was severely beaten at the weekend in the Sighthill area where a large number of asylum seekers are housed.
Building bridges
Strathclyde Police said that many refugees were simply too afraid to go outside after dark.
Its officers are now attempting to build bridges with the asylum seeker community.
They will be patrolling the streets of Sighthill with an interpreter to help police overcome communication barriers.
The project is thought to be the first of its kind in Britain and is said to have led to an immediate improvement in race relations in the area.
Glasgow City Council discussed a possible extension of the programme and other measures to combat racism with the SRC at a meeting on Wednesday.