The 30-year-old was taken to hospital “for assessment” after police were called to Salford on Sunday.
Lennon is now “receiving care and treatment for a stress-related illness”, his club has said.
The England international, who joined Everton from Tottenham in 2015, has not played for the first team since February.
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.”
News of Lennon’s admission has led to an outpouring of support on social media from those involved in the game, as well as fans of his current and former clubs.
Lennon’s representative, Base Soccer Agency, tweeted: “Everyone at Base Soccer sends their support to @AaronLennon12 – get well soon and stay strong.”
Sport shows support for Lennon
Ex-Liverpool and Aston Villa striker Stan Collymore, who has been affected by depression
Thoughts and love with Aaron Lennon and his family right now. I know that place, and I know he’ll be fine with good support from us all.
Former Manchester City midfielder Trevor Sinclair
Thoughts with Aaron Lennon right now.
Former Aston Villa forward Darren Byfield
Hope Aaron Lennon will be OK and gets the help he needs.
England cricketer Kate Cross
Fingers crossed Aaron Lennon is OK. Another reminder that mental health affects us all. Be kind.
Former Watford and Sheffield United striker Danny Webber
Get well soon Aaron Lennon.
BBC’s Juliette Ferrington
Hope Aaron Lennon gets all the help, love and support he needs in every way possible.