Prime Minister Benjamin Netanyahu of Israel on Sunday dismissed a senior minister recently convicted of tax fraud to comply with a Supreme Court ruling that disqualified the minister from serving, shaking the right-wing government just weeks after it came to power.

By complying with the court’s ruling to remove the minister, Aryeh Deri, Mr. Netanyahu avoided an instant, head-on clash with the judiciary at a time when the country is already locked in a fierce debate over government plans for a judicial overhaul. Tens of thousands of Israelis have taken to the streets in recent weeks to protest against the plans to limit the judiciary’s powers, seen by many as a challenge to Israel’s democratic system. About 130,000 protesters came out on Saturday night in Tel Aviv and other cities, according to the Israeli news media.

“I am forced, with a heavy heart, great sorrow and a very difficult feeling, to remove you from your position as a minister in the government,” Mr. Netanyahu wrote in a letter to Mr. Deri that the prime minister read out in his weekly cabinet meeting, with Mr. Deri in attendance.

“I intend to seek any legal way for you to be able to continue to contribute to the state of Israel with your great experience and skills, in accordance with the will of the people,” Mr. Netanyahu added.

But Mr. Netanyahu, himself on trial for corruption, faces the predicament of how to compensate Mr. Deri, the leader of Shas, an ultra-Orthodox Sephardic party, and a close political ally whose support is key to the stability and survival of the coalition government.

A veteran politician, Mr. Deri was one of the most experienced and politically moderate ministers in what has shaped up to be the most far-right and religiously conservative coalition in Israel’s history. The 11 seats that Shas won in the November elections are crucial to the government’s majority in the 120-member Parliament; the coalition parties together control 64 seats.