According to the public relations office of the forum, Ayatollah Mohsen Araki in a statement described the executions as a big crime committed by Bahraini rulers, saying it would bring about the collapse of the Bahraini dictatorship.
He also expressed condolences to the families of the three martyrs, Bahraini scholars and clerics, including Ayatollah Sheikh Isa Qassim, and the nation of Bahrain.
The three Shias faced the firing squad, six days after a court upheld their death sentences over allegations of involvement in a bomb attack in March 2014.
Bahrain, which has been ruled by the Al-Khalifa dynasty, has a majority Shia population which has long complained of marginalization.
It has been rocked by sporadic unrest since March 2011 when security forces brutally crushed an Arab Spring-inspired uprising.
The executions triggered protests in the tiny Persian Gulf country, where demonstrators blocked roads with burning tires and police retaliated by firing tear gas, according to posts on social media.
The protests have continued for days and are reported to also continue through Tuesday.