The Yorkshire-born Premier League star, who has 21 caps for England, was taken to hospital on Sunday to be assessed after officers were called to a road in Salford.
His club said he was being treated for a "stress-related illness" and his representative urged him to "stay strong".
The footballer last played for Everton as a substitute in the goalless draw at Middlesbrough on February 11.
Lennon joined Everton from Tottenham in 2015 but started his footballing career at his hometown club Leeds United in 2003.
Greater Manchester Police said: "Police were called at around 4.35pm to reports of a concern for the welfare of a man on Eccles Old Road.
"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."
Lennon's representative, Base Soccer Agency, tweeted: "Everyone at Base Soccer sends their support to @AaronLennon12 - get well soon and stay strong."
In a statement reported in the Mail, Everton said: "Aaron Lennon is currently receiving care and treatment for a stress-related illness.
"The club is supporting him through this and his family has appealed for privacy at this time."