"This is not Sweden, and this is not the Swedish way," Prime Minister Stefan Löfven said in response to the attacks.
The new year began in the same way as last year when swastikas were daubed on the main Stockholm mosque.
"My feeling is that this is a planned hate crime intended to intimidate a portion of the population. It is an attack on religious freedom, an attack on the whole of society and I have no option but to classify it as an act of terrorism," said Omar Mustafa, president of the Islamic Association of Sweden.
Stefan Löfven condemned the incident and urged influential figures and the general public to take a stand.
"The most important thing now is that everyone distances themselves from this. I would also like to commend those who have gone out in support. In Sweden there should be no need to be afraid of practicing religion," he said.
The Prime Minister added that the latest attack could be regarded as an indication that Sweden is becoming less tolerant, although recent surveys have indicated the opposite.
"There could be something going on, something we have to be very vigilant for."
Police were called to the mosque in Uppsala at 5.30am on New Year's day after someone threw a Molotov cocktail against the building, starting a fire. Racist graffiti had also been daubed on one of the building's walls.
Omar Mustafa meanwhile directed criticism towards the government.
"It's a serious situation. The government must take action."
Sweden's Minister for Home Affairs Anders Ygeman called for a closer dialogue between the government, the police and Muslim communities in order to overcome the low propensity to report crimes among Muslims in Sweden.
"We have to bridge this gulf in confidence and create models for systematic safety where the reporting of crimes is a part of it. In that respect, I think that synagogues and Jewish communities have come further."
Rallies have been planned in Stockholm, Gothenburg and Malmö on Friday.
"It's important to remember that every time there's been an attack the mosque it has then been treated to a love bomb where people have shown support and sympathy. Most of the population are strongly against this type of attack, and tomorrow we will gather these positive forces," Omar Mustafa said