"This resolution is an unnecessary, risky attempt to weaken my constitutional authorities, endangering the lives of American citizens and fearless service members, both today and in the future", Mr Trump wrote in explaining his Tuesday veto.
The veto is the second of Trump's presidency.
The resolution, which passed the US House of Representatives earlier this month and the Senate in March, was a historic milestone, as it was the first time in history that a measure invoking the 1973 War Powers Resolution reached the president's desk.
Supporters of the War Powers Resolution argued the USA shouldn't be involved in the war without explicit permission from Congress. Opponents argued the USA does not have "boots on the ground" and is offering noncombat technical assistance to Saudi Arabia, an ally.
Mr Trump said the measure was unnecessary because except for counterterrorism operations against ISIS militants and Al Qaeda in the Arabian Peninsula, the United States is not engaged in hostilities in or affecting Yemen.
The president called the resolution "dangerous".
Lawmakers criticized the president for not condemning the country for the killing of Jamal Khashoggi, a Saudi journalist who lived in the United States and had written critically about the kingdom.
Iran-backed Houthi rebels have been accused of acts that could amount to war crimes and regularly fire drones at Saudi cities. In the Senate the vote was 54 to 46, with seven Republicans voting with Democrats. Congress lacks the votes to override him. The House has voted to end American involvement in the Yemen war, rebuffing the Trump administration's support for the Saudi-led military campaign.
The top Republican on the committee, Rep. Michael McCaul of Texas, acknowledged the dire situation in Yemen for civilians, but spoke out in opposition to the bill. McCaul said it was an abuse of the War Powers Resolution and predicted it could disrupt US security cooperation agreements with more than 100 countries.
Sen. Sanders has led the charge on the Yemen resolution and might make this a larger fixture of his 2020 presidential campaign, now that the president vetoed the resolution. Trump had declared a national emergency so he could use more money to construct a border wall.
The only other veto Trump has issued was his veto of a resolution of disapproval for his emergency declaration to build barriers along the USA border with Mexico.