The City of London police's Intellectual Property Crime Unit says using the Sci-Hub website could "pose a threat" to students' personal data.
The police are concerned that users of the "Russia-based website" could have information taken and misused online.
The Sci-Hub website says it "removes all barriers" to science.
It offers open access to more than 85 million scientific papers and claims that copyright laws should be abolished and that such material should be "knowledge to all".
It describes itself as "the first pirate website in the world to provide mass and public access to tens of millions of research papers".
But Max Bruce, the City of London police's cyber protection officer, has urged universities to block the website on their networks because of the "threat posed by Sci-Hub to both the university and its students".
"If you're tricked into revealing your log-in credentials, whether it's through the use of fake emails or malware, we know that Sci-Hub will then use those details to compromise your university's computer network in order to steal research papers," he said.
The City of London Police, which is the national lead for fraud, has warned that students studying online at home might be vulnerable.
"Students should be aware that accessing such websites is illegal, as it hosts stolen intellectual property," said Det Insp Kevin Ives.
He warned that visitors to the website, whose Twitter account has been suspended, are "very vulnerable to having their credentials stolen".
The police warning says scientific papers could have been obtained by a "variety of malicious means, such as the use of phishing emails to trick university staff and students into divulging their login credentials".
But the Sci-Hub website has previously told the BBC that it provides students with access to research papers for which the subscriptions are "very expensive".
Andrew Pitts, chief executive of the PSI Registry, which highlights "academic piracy", has warned that users "may inadvertently download potentially dangerous content from this illegal site and put the security of their organisations at risk".
The National Cyber Security Centre, part of the GCHQ intelligence service, has warned of the threat of cyber-attacks against universities.
Last autumn the cyber-agency warned of online attacks attempting to "derail" the start of the academic year in universities.