In his interview with Political Thinking, Mr Ahmed said he was concerned about the protests on 7 October and antisemitism against Jewish students.
"Universities and colleges also have a duty to take steps to protect students from harassment and that includes antisemitic harassment," he said.
"And we in the OfS will be prepared to act if we think universities are not meeting those duties."
He said if there was "unlawful support for proscribed organisations" on campus "then that's absolutely not something that freedom of speech protects and it is something that we would expect universities to address".
Universities and colleges must be registered with the OfS if they want certain benefits, including access to student loan funding.
If universities are deemed to have breached the conditions of registration, they can be sanctioned by the OfS.
In March this year, the University of Sussex was fined £585,000 by the OfS for failing to uphold freedom of speech.
The OfS said the university's policy statement on trans and non-binary equality, including a requirement to "positively represent trans people", could lead to staff and students preventing themselves from voicing opposing views.