Venkatesham has been at the club for 14 years and was appointed general manager in 2020.
He explained that it was time for him to “take on another challenge”, with Arsenal now having the opportunity to appoint his successor to take over next summer.
Venkatesham is committed to the club by then and remains focused on his role.
He said: “It’s been a difficult decision, but it’s time for another challenge. This is not the time for goodbyes as I remain focused until my last day and support a smooth transition.
Arsenal co-chairman Josh Kroenke added: “The board fully supports Vinai’s desire to pursue his next challenge.
“Although it is business as usual and everyone is focused on the season ahead, we would like to take this moment to thank him for his contribution and long service.
“Vinai will always be part of the Arsenal family and will always be welcome at the Emirates Stadium.
“Change and succession are things the club is well prepared for.
“The board remains committed to our strategy and will address the change in direction as we continue to drive the club forward.”