Vilks was delivering a lecture on freedom of speech and art in front of some 250 students on May 11 when he was head-butted by a man as an angry group of about 20 people offended by a film he was showing stormed up to attack him.
Police had evacuated the lecture hall but some demonstrators resisted, and officers used tear gas. Two people were arrested.
"That a university lecture is interrupted by violence is a serious thing, regardless of the opinion that provoked the reaction," Folke Tersman, the head of the university's philosophy department, said in Monday's statement.
"It is incompatible with the basic values democracy is based on. It is to uphold these values that we are inviting him again," he added.
Four days after he was attacked at Uppsala University, Vilks' home in the south of Sweden was fire-bombed by two Swedish brothers of Kosovar origin.
They have been convicted and were given jail sentences of two and three years.
Vilks has faced numerous death threats and a suspected assassination plot since his drawing of the Muslim prophet with the body of a dog was first published by Swedish regional daily Nerikes Allehanda in 2007.
It illustrated an editorial on the importance of freedom of expression.
The drawing by Vilks prompted protests by Muslims in the town of Oerebro, west of Stockholm, where the newspaper is based.
Egypt, Iran and Pakistan also made formal complaints about the drawing.
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