The "real reason" for the execution was "that Sheikh Nimr... demanded the squandered rights of an oppressed people," the movement said in a statement.
The statement was also quoted by Hezbollah's official al Manar television and Lebanon-based Al Mayadeen TV.
Sheikh Nimr al-Nimr along with 47 others were executed on Saturday. Sheikh Nimr, a critic of the Riyadh regime, was shot by Saudi police and arrested in 2012 in the Qatif region of Shiite-dominated Eastern Province, which was the scene of peaceful anti-regime demonstrations at the time.