The Navy said a team from the USS Kidd boarded the fishing boat on Thursday, rescued the sailors and took 15 pirates into custody.
The suspected Somali pirates reportedly hijacked the boat nearly two months ago.
Iran has recently protested the presence of the USS Kidd and other ships in the Persian Gulf, because they feared American warships could try to enforce an embargo against Iranian oil exports.
"The rescue of Iranian sailors by American forces is considered a humanitarian gesture and we welcome this behavior," Foreign Ministry spokesman Ramin Mehmanparast was quoted as saying by state TV's Al-Alam Arabic channel.
On the flip side, Iran's hard-line Fars news agency had a different take of the events, saying the rescue operation was a Hollywood dramatization of a routine event.
The Fars report said attacks by Somali pirates in the region are common, and that Iran's navy has freed many mariners held by pirates many times in recent years without much ado.
"Basically, rescuing trading and fishing boats from the hands of pirates in the Arabian Sea and the Gulf of Aden is considered a completely normal issue," Fars said. "A U.S. helicopter filming the rescue operation from the first minute makes it look like a Hollywood drama with specific locations and actors. It shows the Americans tried to publicize it through the media and present the American warship as a savior."
Amid escalating tension with Iran over its nuclear program, the Obama administration reveled in delivering Friday's announcement.
The incident occurred after a week of tough talk from Iranian leaders, including the statement that American vessels were no longer welcome in the Gulf. Iran also warned it could block the Strait of Hormuz, the strategic waterway through which a sixth of the world's oil flows to market.
The Associated Press contributed to this report.