Most states don’t mandate malpractice insurance for physicians. A few require it outright or require participation in a state patient compensation fund, which comes with minimum coverage limits.
The bigger requirement is contractual. Hospitals require proof of coverage for privileges, usually at $1 million / $3 million. Many insurance networks and employers ask for the same. Going without coverage also puts your personal assets at risk in a lawsuit.
Check with your state medical board for current rules, and talk with your broker about what your hospitals and payers require.