The statement named all those who were killed, including several people from large families and tribes in Saudi Arabia.
The interior ministry said the individuals had been found guilty according to the law and ordered executed by the Specialized Criminal Court in Riyadh, which specialises in terrorism trials, and the country's high court.
Among the 37 was Abdulkareem Al-Hawaj, a young Shiite man who was under 18 when his alleged crimes were committed, according to a statement from United Nations human rights experts a year ago.
In January 2016, Saudi Arabia enraged Shiite Iran with the execution of prominent Shiite cleric Nimr al-Nimr, among a group of 47 people convicted of "terrorism".
The mass execution was ratified by a royal decree.
Saudi Arabia generally beheads prisoners condemned to death, in ceremonies performed by executioners using a sword - a punishment in line with the kingdom's strict interpretation of Islamic law.
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Rights group Amnesty International, in a statement, said most of those executed were Shiite men "convicted after sham trials that violated international fair trial standards (and) which relied on confessions extracted through torture".
State-run media, such as the Saudi news channel al-Ekhbariya, aired the statement, according to the outlet.
A number of Saudi analysts and pro-government writers brought in to discuss the executions on al-Ekhbariya said they are a powerful sign that the country's leadership will not hesitate to use the full might of the judicial system to punish Saudis who seek to disrupt the kingdom's security.
The executions by beheading were carried out on Tuesday in the regions of Riyadh, Makkah, Madinah, Eastern Province, Qasim, and Asir. Among those executed was a young man who was convicted of a crime that took place while he was under the age of 18.
People convicted of terrorism, homicide, rape, armed robbery and drug trafficking face the death penalty, which the Saudi government says serves as a deterrent against serious crime. Public displays of the bodies of executed men last for around three hours until late afternoon prayers, with the severed head and body hoisted to the top of a pole overlooking a main square.
Security forces in the kingdom have been a frequent target of attacks perpetrated by the al-Qaeda and Islamic State groups, Bloomberg reported. The attack was claimed by the militant Islamic State group.
Saudi Arabia's prosecution of Shiites, who have complained of discrimination in the kingdom, has aggravated the rivalry.