This is after she posted a note on Facebook accusing Hall of supplying Prince with drugs "over the decades" and of spiking her with drugs.
The suit, filed in Los Angeles on Thursday, is seeking damages of "not less than" $5 million.
"Desperate, attention seeker Sinead O'Connor has maliciously published outlandish defamatory lies about comedian Arsenio Hall, falsely accusing him of supplying illegal 'hard drugs' 'over the decades' to the recently deceased music artist, Prince, and of spiking her with drugs once years ago," the lawsuit says.
On Monday, O'Connor, who is no stranger to controversy,
accused Hall of supplying Prince with drugs.
"Two words for the DEA investigating where prince got his drugs over the decades ... Arsenio Hall. Anyone imagining prince was not a long time hard drug user is living in cloud cuckoo land," O'Connor wrote in a post that has since been deleted.
"Arsenio I've reported you to the Carver County Sheriff's office. Expect their call. They are aware you spiked me years ago at Eddie Murphy's house. You best get tidying your man cave."
Hall has denied the "heinous accusations" in the lawsuit, calling O'Connor's statement "despicable, fabricated lies."