In his resignation letter, addressed to the Prime Minister, Streeting writes that he has lost confidence in the party's leadership and that it would be "dishonest and unprincipled" to remain a minister.
"Where we needed a vision, we have a vacuum. Where we need leadership, we float free," he writes.
"It is now clear that you will not lead the Labour Party into the next general election."
Hours earlier, Keir Starmer had announced through a spokesperson that he was prepared to fight to stay in power.
Streeting did not say whether he intended to challenge Starmer or not. According to previous reports in the British media, he had prepared his resignation as a minister in order to be able to mount a serious bid for the Labour leadership. But sources close to Streeting tell Sky News that the former health minister has no intention of challenging Starmer at this time.
Pressed
The Prime Minister responded in his own letter on Thursday evening that he was "sincerely saddened" by Streeting's resignation and that he hoped they could both work together to address the problems.
Demands for Keir Starmer's resignation have been mounting in recent days following the Labour Party's major defeats in regional and local elections - in addition to the crisis of confidence surrounding Starmer's appointment of former Labour minister Peter Mandelson, who turned out to have links to the late convicted sex offender Jeffrey Epstein.
During Wednesday's State Opening of Parliament, Starmer was met with criticism from both the opposition and his own members. During the debate that followed the grand State Opening, Conservative MP Kemi Badenoch, in particular, called for Starmer to resign.
Streeting is the fifth minister to leave the government this week, but the first believed to be eyeing the party leadership position.
Aiming for leadership
Streeting, 43, has made no secret of his ambitions to one day take on the role of Labour leader, but he has been cautious during Starmer's confidence crisis, repeatedly denying that he intends to challenge the prime minister.
The outgoing health minister is considered an effective public speaker and has been regularly sent out to defend the government in the press, according to the BBC.
Within the Labour Party, he has garnered support mainly from the centre and right. He was a prominent critic of the party's leftward shift under Jeremy Corbyn and campaigned to remain in the EU in the Brexit referendum.
