"The Saudi government is killing innocent people, women and children in Yemen ... and Americans support these immense crimes," Khamenei said in a speech to students quoted on his official website.
Iran, the Shiite rival of Sunni-ruled Saudi Arabia, has strongly condemned the nearly six-week-old coalition air strikes against Shiite Huthi rebels who have seized large parts of Yemen including the capital.
Washington has given intelligence and logistical support to the coalition.
Tehran is a key ally of the Huthi rebels but denies arming them.
"The Americans shamelessly support the killing of the Yemeni population, but they accuse Iran of interfering in that country and of sending weapons when Iran only seeks to provide medical and food aid," Khamenei said.
Signup to our newsletter and follow us on Facebook and Twitter!
"The revolutionary people of Yemen do not need weapons because they control all the country's military bases and centres," he added.
Tensions between Riyadh and Tehran have been rising steadily, not only over Yemen but also the situation in Syria, Iraq, Lebanon and Shiite-majority but Sunni-ruled Bahrain.
The United Nations says at least 1,200 people have been killed in Yemen since March 19, and has repeatedly warned that the already impoverished Arabian Peninsula state faces a major humanitarian crisis.
US Secretary of State John Kerry said Wednesday in Djibouti on his way to Saudi Arabia that he would talk to Riyadh about a "humanitarian pause" in military operations in Yemen to facilitate aid operations.
The Iranian authorities have announced planned demonstrations on Friday across the country against "the crimes of the Saudi government and to support the Yemeni people".