Ukrainian army helicopter pilot Savchenko is accused in the June 2014 killing of two Russian journalists in her war-torn country's separatist east.
Russian prosecutors have demanded a 23-year jail sentence for the 34-year-old former Ukrainian volunteer battalion member.
Russia's trial of Savchenko has been condemned by Kiev and the West as a political sham.
The Ukrainian president's website said Maryna Poroshenko asked the US first lady in a letter to make her views about the case clear to the Russian government.
"Dear Michelle, I hope that your voice will join the international campaign to free Nadiya Savchenko and let her return home," the president's website quoted the letter as saying.
"Maryna Poroshenko stressed that... Savchenko served side by side with US servicemen and risked her life in order to restore democracy and order in Iraq," the presidential website added.
Savchenko joined the Ukrainian army in 2003 and became a paratrooper -- a position that made her the only female combat soldier among the 1,690 people Kiev sent to support the US-led military campaign in Iraq.