The two brothers, aged 19 and 21, are believed to have attacked Vilks' house in the village of Nyhamnsläge in southern Sweden on Friday night with gasoline-filled plastic bottles. A window in the house was smashed and a curtain was set on fire.
In addition, attempts were made to build two fires along the façade. The artist himself was not at home at the time.
The 21-year-old was arrested late on Saturday and the 19-year-old on Sunday morning.
"He is of Swedish nationality but originally from Kosovo...He was unknown to the police so far," Skåne district police spokesman Calle Pärsson told new agency AFP regarding the 21-year-old.
The attempted arson followed an attack on Vilks during a lecture at Uppsala University last Tuesday, where he claims to have been head-butted in the chest.
Three suspects, two men and one woman, arrested after the alleged assault were later released after several hours in custody.
The artist's website has meanwhile also been targeted by hackers in recent days with his webmaster referring to the repeated intrusions as a "game of cat and mouse".
Visitors to vilks.net on Tuesday morning were greeted with a message saying that the site administrators are "working hard to get the page back on its feet", claiming that the hacks originate from an Islamic group calling itself Al Qataari.
Lars Vilks courted global attention in 2007 when the Swedish regional daily Nerikes Allehanda published his satirical cartoon depicting Muhammad as a dog to illustrate an editorial on the importance of freedom of expression.
The cartoon prompted protests by Muslims in the town of Örebro in central Sweden, where the newspaper is based, while Egypt, Iran and Pakistan made formal complaints.
An Al-Qaeda front organisation then offered $100,000 to anyone who murdered Vilks - with an extra $50,000 if his throat was slit - and $50,000 for the death of Nerikes Allehanda editor-in-chief Ulf Johansson.
The protests in Sweden echoed the uproar in Denmark caused by the publication in September 2005 of 12 drawings focused on Islam, including one showing the prophet Muhammad with a turban in the shape of a bomb.
In March, US citizen Colleen LaRose, who called herself "JihadJane" in a YouTube video, was charged by US authorities with conspiring to kill Vilks after seven suspected co-plotters were arrested in Ireland.