Speaking to British ITV channel, Rob Weinwright said the attack had so far affected more than 100,000 organizations in 150 countries.
He warned the threat could escalate further and expressed concerns over possible attacks on Monday.
"We are in the face of an escalating threat, the numbers are going up,” he said.
The unique virus type known as ransomware locks computer screens with a message demanding $300 worth of bitcoins -- a special type of online currency -- to unlock the systems.
"Most people are not paying this, so there ain't a lot of money being made with this by criminal organizations so far," the Europol chief said.
Wainwright said Europol was working on the basis the cyberattack was carried out by criminals rather than terrorists.
The cyberattack has severely affected Britain’s healthcare services. Services in as many as 45 healthcare centers, including hospitals under Britain’s National Health Services (NHS) came to a halt.
On Saturday, NHS Digital said: "We are continuing to work around the clock to support NHS organizations that have reported any issue due to yesterday's cyber-attack."
Weinwright said the impact on U.K.’s healthcare services only proved that all sectors must take cyber security "absolutely seriously".
He underlined that healthcare services in many countries remain particularly vulnerable to such attacks.
"We have been cornered for some time that the healthcare sector in many countries are particularly vulnerable. They're processing a lot of sensitive data, very often on legacy systems," he said.
He said banks had so far not borne the brunt of the attack.
"Very few banks, if any in Europe, have been affected by this and that's because they've learned through painful experience about being the number one target for cybercrime, the value of having a proper strategy in place," Weinwright said.
Meanwhile, Turkey’s Information and Communications Authority BTK said on Saturday an operation to prevent further spread of the malware continued and urged people to update their antivirus programs and scan their computer systems.