The state was removed on Friday in Buraydah (220 miles north west of the capital Riyadh), the provincial capital of Qassim.
Mosques are currently the only lawful places of worship in Saudi Arabia, however, some discreet Christian services have been held without interference.
Pictures shared on social media appear to the rubble of the statue.
Speaking in the pan-Arab newspaper, Al-Hayat, commentator Akal Al-Akal criticised the demolition of the landmark, which is thought to have stood for 25 years.
#Wahhabi #Saudi authorities blow up a 25 yrs old decorative art work because it resembles a '#cross' in #Buraydah,Qaseem,birthplace of #ISIL pic.twitter.com/Awf2w5YrDT
— LeoOfArabia (@AynHaAyn) April 19, 2017
He said those behind its removal are "playing on the emotions and feelings of the local public", adding that the motivation may have been about "inciting public opinion about life in Saudi Arabia as it embarks on a real opening for the arts."
He added: "We must respect the symbols of other religions, just as we seek similar treatment in other countries."
Under a move led by Deputy Crown Prince Mohammed bin Salman and at the angst of some ultraconservatives, Saudi Arabia has been embracing the arts more widely recently.
According to AP, municipal officials in the city were not immediately available to comment.