The 30-year-old England international, who joined Everton from Tottenham Hotspur in 2015, has not featured for the Merseyside club since the goalless draw at Middlesbrough in February.
Earlier last month, Everton manager Ronald Koeman said Lennon was “not in a physical way to be part of the team”.
“Aaron Lennon is receiving care and treatment for a stress-related illness,” the club said in a statement.
“The club is supporting him through this and his family has appealed for privacy at this time.”
Responding to a call in nearby Salford, the Greater Manchester Police said a man taken to hospital for “assessment” on Sunday.
“Police were called at around 4:35 p.m. to reports of a concern for the welfare of a man on Eccles Old Road,” a police statement said.
“Officers attended and a 30-year-old man was detained under Section 136 of the Mental Health Act and was taken to hospital for assessment.”
Base Soccer Agency, which represents Lennon, tweeted: “Everyone at Base Soccer sends their support to @AaronLennon12 — get well soon and stay strong.”