Karoline Leavitt, the White House press secretary and one of the administration’s strongest public defenders of its aggressive immigration enforcement policies, found herself unexpectedly entangled in the fallout of a late-night Immigration and Customs Enforcement operation after a member of her extended family was taken into custody, according to three people familiar with the matter.

The incident, which became public after a video circulated on several social media platforms early Wednesday, immediately injected personal stakes into an issue Ms. Leavitt has championed from the briefing room podium. It also sent senior administration officials scrambling to assess the political ramifications of an enforcement action that appeared to catch both the White House and Ms. Leavitt off guard.

A spokesperson for ICE declined to comment on individual enforcement cases but said the agency “conducts operations based on established priorities and legal authorities, without regard to political affiliations.” The White House also declined to comment, and Ms. Leavitt has not publicly addressed the matter.

People close to the family, who spoke on the condition of anonymity to discuss a developing situation, said relatives were “shaken” and had sought guidance from both immigration attorneys and White House aides. Some family members posted brief pleas for assistance on social media before later removing the messages.

Inside the West Wing, the episode prompted what one senior official described as “a moment of real concern” about both optics and timing, as the administration continues to face criticism for its broadened enforcement efforts. Several aides, speaking privately, said they were surprised that such an operation could intersect so directly with a prominent public face of the administration.

Ms. Leavitt, 28, has risen quickly in Republican politics and has frequently defended the administration’s approach as necessary for national security and immigration control. Her responses in recent weeks have emphasized that the White House “will not apologize for enforcing the law.”

All of that lent an unusual degree of attention to her silence on Wednesday. Analysts across the political spectrum noted that Ms. Leavitt now confronts a political and personal dilemma rarely faced by senior communications officials: how to maintain message discipline while navigating a situation affecting her own family.

“It puts her in a virtually unprecedented position,” said Steven Billet, a public policy professor at George Washington University. “The administration relies on her to communicate its most controversial policies. Now she has a direct personal connection to one of them.”

It remains unclear whether the case involving Ms. Leavitt’s relative aligns with the enforcement categories the administration has emphasized, or whether it reflects broader, more discretionary operations that critics say have expanded in recent months.

For now, aides and allies say the press secretary is focused on managing the situation privately, even as the political world watches closely.

The White House is expected to face questions about the incident in upcoming briefings, where Ms. Leavitt will once again take her place behind the lectern — this time under far more complicated circumstances than she or the administration anticipated.