Two of the four are additionally suspected of planning terrorist attacks.
Three of the men were arrested in Switzerland and have been jailed since spring 2014, the 24 heures newspaper reported online.
The man named as the principal suspect, a paraplegic who relies on a wheelchair to get around, arrived in Switzerland in 2012 and obtained asylum.
The 30-year-old is thought to have joined a terrorist organization in Iraq as early as 2004, the paper said.
Hospitalized in Schaffhausen in the north east of the country before being moved to a centre for paraplegics in the canton of Aargau, he is said to have maintained close links with this organization and to have planned terrorist attacks.
Despite operations and rehabilitation, the Iraqi was active on social media platforms and posted videos supporting sharia law and terrorism, according to the prosecution.
The indictment does not say where the group planned to stage its attacks, but says intercepted conversations made it clear they were to be carried out in the name of IS.
The investigation and arrests were triggered by intelligence from the United States that and Islamic State cell planned an attack on Swiss soil.
In July last year a fourth suspect was detained on suspicion of travelling to Syria to deliver communications devices to IS.
He is also accused of deleting evidence of his links with IS on Facebook.
Last November the Swiss Attorney General's Office said active criminal proceedings were underway against 33 individuals over suspected ties to extremist Islamist groups.
The trial is expected to last all week.