Turkey’s President Recep Tayyip Erdogan late Monday accepted the resignation of his finance minister and son-in-law, Berat Albayrak, parting with a relative whose tenure was marred by currency crises, but whose departure coincided with a strong rally of the Turkish lira.

Mr. Erdogan’s office said the president had accepted Mr. Albayrak’s request to be excused from his duties. The statement came more than 24 hours after Mr. Albayrak said in a surprise Instagram post that he was stepping down for health reasons. In a decree published Tuesday, Mr. Erdogan named an engineer, Lufti Elvan, as finance minister.

In itself, the designation of a new minister doesn’t herald a shift in policy because the president has consistently said that he was in charge of running the economy, describing his subordinates as mere executors. Still, Mr. Albayrak’s exit could help quell growing rancor within Mr. Erdogan’s ruling Justice and Development Party that the rise of a “damat,” or son-in-law, to the top of Turkish politics carried the hallmark of nepotism.

Some Turkish officials said that Mr. Albayrak quit because he was upset to have been kept in the dark about Mr. Erdogan’s weekend decision to dismiss the governor of the central bank. An aide to Mr. Albayrak declined to comment.

While confusion reigned over Mr. Albayrak’s fate for much of Monday, the lira enjoyed a rare feat, gaining as much as 5.8% against the U.S. dollar on investor expectations that the new governor, Naci Agbal, would raise interest rates to combat inflation and support the lira.