Trump issued the warning on Friday after ICC judges rejected a request by the court's prosecutor to probe atrocities committed by US forces in Afghanistan.
Trump hailed the unusual ruling as a "major international victory," claiming that the Americans and Israelis should be immune from ICC prosecution.
"Since the creation of the ICC, the United States has consistently declined to join the court because of its broad, unaccountable prosecutorial powers; the threat it poses to American national sovereignty; and other deficiencies that render it illegitimate," he said in a statement.
"Any attempt to target American, Israeli, or allied personnel for prosecution will be met with a swift and vigorous response," he added.
However, Amnesty International denounced the ICC's decision as a "shocking abandonment of victims" that would "weaken the court's already questionable credibility."
Biraj Patnaik, South Asia Director at Amnesty International, stressed that the ruling would be seen as a "craven capitulation to Washington's bullying."
Last month, US Secretary of State Mike Pompeo announced that the US would withdraw or revoke visas for ICC staff who prosecute American troops in Afghanistan as well as their allied personnel, including Israelis.
He also warned about potential economic sanctions "if the ICC does not change its course."
US National Security Adviser John Bolton had also threatened to revoke the visas of ICC personnel if the court pursued charges against members of the US military over crimes in Afghanistan.
Earlier this month, the US revoked ICC prosecutor Fatou Bensouda's visa as part of a crackdown on the ICC.