The pastor of a prominent evangelical megachurch near Dallas abruptly announced an indefinite leave of absence on Sunday, effective immediately, because of an online relationship he had with a woman who is not his wife.

Matt Chandler, the lead pastor of the Village Church, told his congregation in a tearful admission that took place on stage during the worship service, that the relationship was not “romantic or sexual” but “unguarded and unwise,” and included “coarse and foolish joking that’s unbefitting of someone in my position.”

The sudden departure under somewhat murky circumstances of the high-profile pastor, admired by many younger evangelicals for his preaching and dynamic stage presence, is the latest crisis of leadership in American evangelicalism.

The announcement of Mr. Chandler’s departure did not include allegations of abuse. But it comes as his church’s larger denomination, the Southern Baptist Convention, faces continued scrutiny for its handling of a sprawling sexual abuse crisis.

Southern Baptist leaders said earlier this month that multiple branches of the denomination were under investigation from the Justice Department for sexual abuse.

In May the denomination released a report from a third-party investigation that found that national leaders had suppressed reports of sexual abuse and resisted proposals for reform over two decades.

The convention, the largest Protestant denomination in the United States, is also grappling with internal divisions over its direction — including fundamental questions around the role of women in ministry and leadership.

After reviewing the report, church leaders decided that his actions had violated the church’s social media policy and biblical standards of being “above reproach,” but did not disqualify him from leadership. Church leaders decided he should take a leave that was both “disciplinary and developmental,” the statement said.

The church declined to share a copy of the report, “because we want to honor the request of the woman Matt was messaging with not to be in the spotlight,” the church said in an email.