Under the law, people who refuse to give samples for the test face one year in jail and a fine of up to $33,000 (29,700 euros). Those who provide fake samples can be jailed for seven years.
Parliament also approved a $400 million emergency funding for spending required by the interior ministry.
"We have approved the DNA testing law and approved the additional funding. We are prepared to approve anything needed to boost security measures in the country," independent MP Jamal al-Omar said.
A suicide bomber blew himself up during Friday prayers last week at a Shiite mosque in the capital, also wounding 227 people, in an attack claimed by the Islamic State group.
IS`s Saudi affiliate, the Najd Province, claimed the bombing and identified the assailant as Abu Suleiman al-Muwahhid. Kuwaiti authorities said his real name was Fahd Suleiman Abdulmohsen al-Qabaa, saying he was a Saudi born in 1992.
Interior Minister Sheikh Mohammad Khaled al-Sabah told parliament Tuesday security agencies had busted the "terror cell" behind the bombing.
"We are in a state of war. Yes, we have busted this terror cell but there are other cells we are going to strike," Sheikh Mohammad said.
He said the emirate has revised "all security measures, especially around mosques and all places of worship".
Of an unspecified number of suspects arrested, five have been referred to the public prosecution service. They include the driver who took the bomber to the mosque and the owner of the car.
Justice and Islamic Affairs Minister Yacoub al-Sane told parliament the supreme judicial council has decided to create a special court to try the case.
IS considers Shiites to be heretics.
In May, the group claimed responsibility for two similar bloody attacks against Shiite mosques in Saudi Arabia and has carried out several deadly anti-Shiite attacks in Yemen.
In Shiite-majority Bahrain, the interior ministry was recruiting "security volunteers" to protect places of worship in the Sunni-ruled kingdom, the official BNA news agency reported.
So far, there have been no attacks on Shiite mosques in the tiny kingdom.
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