In an interview with The Sunday Times, Vaizey said the station was failing to reach young listeners and said he wanted to see its licence put up for auction.
Vaizey said: "Radio 1 is not fulfilling its obligation to its audience. Its median age is those in their thirties when it should aim much more at teenagers and [those in] their twenties.
"There is then a good argument for the BBC to be rid of Radio 1 and give the commercial sector a chance to use the frequency."
The station's frequency is said to be worth at least £100m and would be a prize for the commercial sector.
However, the office of Jeremy Hunt, the shadow culture secretary, said that the sale of Radio 1 was not Conservative policy and that the station was safe if the Tories came into power.
Vaizey told The Sunday Times that the Tories would also scrap the ban on product placement on commercial channels, such as ITV, and increase the amount of time available for ads each hour.
Analysts believe that product placement could raise an extra £50m each year for ITV alone.
Vaizey's comments differ from those made last year by Andy Burnham, then culture secretary, who said the UK would not be adopting an amended EU directive on broadcasting, which reversed the Europe-wide ban on product placement.
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