Kan announced his resignation in a Slack message which was viewed by Reuters. The company and Kan offered no other details.
In his message to employees Kan noted that Cruise had been serving 10,000 rides per week. "I know Cruise will achieve that again soon," he wrote.
The new exit comes at a tumultuous time for self-driving taxi maker Cruise, which is undergoing a safety review of its U.S. fleet, leading to Vogt's resignation Sunday.
In a live-streamed meeting Monday, GM executives, including CEO Mary Barra, did little to assuage employees' concerns, people who listened told Reuters. The company did not address a long list of questions workers had compiled concerning Cruise's future or about a controversial plan to halt a share resale program.
"They shared nothing of substance," one of the people who listened to the meeting told Reuters.
Similarly, in his resignation announcement, Vogt, 38, offered little in the way of explanation.
"I have resigned from my position," he wrote in an email to staff viewed by Reuters on Sunday. Barra in Monday's meeting said Vogt had resigned of his own accord.
Cruise's woes are also a setback for an industry dependent on public trust and the cooperation of regulators. The unit had in recent months touted ambitious plans to expand to more cities, offering fully autonomous taxi rides.
Vogt's resignation came after GM and the board at Cruise increased their scrutiny of its leadership.
Cruise is retrenching after an October accident that ended with one of Cruise's self-driving taxis dragging a pedestrian. Cruise pulled all its vehicles from testing in the United States to conduct a safety review.
Kan did not immediately respond to a request for comment Monday.
Vogt over the weekend apologized to staff for the company's continuing troubles. "I take responsibility for the situation Cruise is in today," he wrote in an email. "There are no excuses, and there is no sugar coating what has happened."
GM shuffled leadership at Cruise including naming general counsel Craig Glidden as chief administrative officer, bringing in a third-party safety officer and appointing co-presidents.
Autonomous vehicle regulation is still nascent and largely overseen state by state. U.S. Transportation Secretary Pete Buttigieg told reporters on Monday the federal government will do everything it can using existing regulatory powers to ensure that Cruise and other autonomous vehicles are deployed safely.
