The announcement by Prime Minister Pedro Sanchez comes amid a wider crackdown on online platforms, with regulators accusing them of practices ranging from anti-competitive behaviour in digital advertising to deliberate design of addictive features.
TikTok said later on Tuesday that child sexual abuse material was "abhorrent and categorically prohibited on our platform".
"TikTok has robust systems in place to thwart attempts to exploit or harm young people, and we continue to prioritise and invest in advanced technologies to stay one step ahead of bad actors," a spokesperson for the company said in a statement.
X and Meta did not immediately respond to requests for comment.
The move - the first from a package of social-media regulations Sanchez unveiled at a government summit in Dubai earlier this month - was based on a technical report from three ministries, his office later said in a statement.
Government spokesperson Elma Saiz told reporters authorities "cannot allow algorithms to amplify or shelter" such crimes, adding that children's safety, privacy and dignity were at risk.
Separately on Tuesday, Ireland's Data Protection Commission said it had opened a formal investigation into X's xAI chatbot Grok over the processing of personal data and its potential to generate harmful sexualised images and video, including of children.
The DPC is the lead EU regulator for Elon Musk's X because the U.S. company's EU operations are based in Ireland.
One in five young people in Spain - mostly girls - say fake nude images of themselves were created by AI and shared online while they were minors, Sanchez's office said, citing rights group Save the Children.
"These platforms are undermining the mental health, dignity, and rights of our children," Sanchez wrote on X. "The state cannot allow this. The impunity of these giants must end."
The Justice Ministry would ask prosecutors to "investigate the crimes that X, Meta, and TikTok may be committing through the creation and dissemination of child pornography using their AI".
Spain is not the only country cracking down on social media platforms. Other governments have opened investigations, imposed bans and sought safeguards in a widening global push to curb illegal material.
The European Commission is investigating Meta, TikTok and Grok under the European Union's Digital Services Act, while France, Brazil and Canada have filed complaints against Grok over illegal content distribution.
Two weeks ago, Sanchez outlined new measures to tackle online abuse and protect children, including an Australian-style ban on social-media access for those under 16.
