The Russian daily Sport Express reported Ufa manager Viktor Goncharenko will be appointed as his replacement.
CSKA play the Premier League side at Wembley with both clubs already out of the Champions League but with a Europa League spot up for grabs, while CSKA are third in the Russian Premier League.
"CSKA would like to thank Leonid Slutsky for seven years of his effective cooperation with the club, for three national titles, two Russian cups and two Super Cups," said a statement Tuesday on the club's website.
"We also thank you for all of these unbelievable emotions that your team have presented to its supporters throughout these years.
"The club's doors will always be open to you."
There was no immediate announcement on Slutsky's successor but Russian daily Sport Express reported Ufa manager Viktor Goncharenko will be appointed as his replacement.
"I'd like to thank everybody in the club and express my confidence that I don't say 'farewell' to the club, I just say 'goodbye'," said Slutsky.
"Seven years at the helm is a huge period of time and all of these years were definitely the best in my career.
"I think I can be proud of my work at the club. Not only by winning the titles but also with the fact that we've finished in the Russian league's top three in all of my six full seasons as CSKA manager starting from 2010.
"It's an enormous mark of stability under the existing conditions in the Russian league. I'm proud that I've worked for such a club as CSKA."
Slutsky, 45, previously coached Russian top-flight sides Uralan Elista, FC Moscow and Samara before taking over at CSKA in October 2009.
He led the Red Army outfit to domestic titles in 2013-14 and 2016, Russian cups in 2011 and 2013 and the country's Super Cup in 2013 and 2014.
He also simultaneously took charge of Russia's national team in August 2015.
However, Slutsky resigned from that post in June after Russia crashed out of Euro 2016 without a win.