Oliver Dowden, Secretary of State for Digital, Culture, Media and Sport (DCMS), praised the drama as a “beautifully produced work of fiction”.
But he raised concerns that younger viewers might mistake the fictional depictions, built around the royal family, for real-life happenings.
He told the Mail on Sunday: “It’s a beautifully produced work of fiction, so as with other TV productions, Netflix should be very clear at the beginning it is just that.
“Without this, I fear a generation of viewers who did not live through these events may mistake fiction for fact.”
The newspaper said Mr Dowden is expected to write to Netflix to request a reference at the start of episodes making clear the drama is fictionalised.
DCMS did not have any comment on Saturday.
Mr Dowden’s remarks come after a similar suggestion from Earl Spencer, the brother of Diana, Princess of Wales.
He told ITV’s Lorraine: “I think it would help The Crown an enormous amount if, at the beginning of each episode, it stated that: ‘This isn’t true but it is based around some real events’.”
He added: “I worry people do think that this is gospel and that’s unfair.”
The drama recently came in for criticism from the widow of a major killed in a Swiss ski resort, who said she was “very upset” to learn the disaster features in the latest series, after asking producers not to include it.
Major Hugh Lindsay, a friend of the Prince of Wales and a former Queen’s equerry, died in an avalanche at the Swiss resort of Klosters in 1988.
His widow Sarah Horsley said she was “horrified” when she was told the episode was going ahead and was concerned about the impact on her daughter.