Zimmer told reporters on Friday that Griffen would not be able to return to practice ahead of Minnesota's Week 5 game with Philadelphia on Oct. 7.
On Thursday, Griffen posted a lengthy message on Instagram. He used his social media to address the events leading to his mental health issues and thanked his family, friends and teammates.
Last week, ESPN reported that the Vikings sent Griffen a letter saying he could not return until getting his mental health evaluated.
Griffen has been dealing with a mental-health-related issue for the last few weeks and currently is being evaluated at a hospital, NFL Network's Tom Pelissero reported.
Vikings' executive director of player development Les Pico told police in Minnetrista, Minn., that the team had sent Griffen and his agent the letter on Thursday, informing him he could not return until receiving an evaluation.
That letter was sent two days before an alleged incident involving Griffen at a Minneapolis hotel.
. In a separate incident report obtained by ESPN, the Minneapolis Police Department was called Saturday to Hotel Ivy because an individual was threatening to shoot someone if he wasn'tt allowed in his room. According to ESPN, the person in question at the hotel was Griffen.
After that incident, Griffen allegedly tried to break into the home of Vikings teammate Trae Waynes.
Griffen played in the Vikings' first two games and had half a sack in each game, but Pelissero reported that the situation became "unmanageable" in Week 3, and he did not play against the Buffalo Bills.
According to the incident report, Pico told police before the incident at the hotel that Griffen had been "explosive, screaming and yelling" at the team facility.
Vikings general manager Rick Spielman said Monday night in a statement that the team was "currently focused on Everson's well-being and providing the appropriate support for him and his family."
Zimmer referred to Spielman's statement before saying on Tuesday, "The only thing I'm really concerned about has nothing to do with football."
"He's always been a really, really good model for us, and obviously he's going through some tough times right now," the coach added.
Griffen signed a four-year, $58 million contract extension with the Vikings in 2017.
He has been named to the Pro Bowl each of the past three years and has 62 career sacks.