The Dutch defender takes over from Cristian Romero, with Pedro Porro appointed vice-captain. Ben Davies, James Maddison and Archie Gray will also form part of Tottenham's leadership group.
De Zerbi explained that he wanted several players to take responsibility within the team.
"The new captain is Micky van de Ven. Second is Pedro Porro, third Ben Davies, fourth James Maddison and fifth Archie Gray," De Zerbi said.
"Why five? Because I want as many captains inside the pitch and to be clear in the situation and the position. Every one of them deserves to be captain or in the group of captains."
Van de Ven, however, will not lead Tottenham out against Brentford after being ruled out of the opening league fixture, while Porro is also unavailable.
De Zerbi confirmed that Maddison, Dominic Solanke and Destiny Udogie are available, but Pape Matar Sarr will miss the game after feeling pain in his hamstring or glute.
"Nothing important, but we don't take risks with him, especially at this moment," De Zerbi said.
Tottenham will be looking for a strong start after finishing 17th last season, while Brentford ended the previous campaign in ninth.
The fixture also presents Tottenham with a difficult test away from home, with Brentford having established themselves as a competitive Premier League side since returning to the top flight in 2021.
De Zerbi has also overseen major changes to his squad during the transfer window, with Tottenham having made two record-breaking midfield signings in Mateus Fernandes and Sandro Tonali.
The club have also been linked with Manchester City winger Savinho, Liverpool forward Cody Gakpo and City attacker Omar Marmoush.
De Zerbi refused to discuss individual transfer targets but suggested Tottenham's business was not finished.
"It's not right to speak about players until they are official. Just to say I'm very happy. We have not finished yet in the transfer market. It's an important part," he said.
"So far, we have had great signings, great players, great behaviour, great spirit and great personality."
The Italian also stressed that Tottenham cannot rely simply on the quality or reputation of their new arrivals.
"You know better than me in the Premier League you don't win games with names and big players," De Zerbi said.
"You have to deserve to win the game. To deserve to win the game, we have to reach the right level in character, intention and value and in the style of play as well."
