The winner will receive a pair of Club Wembley seats, worth about £18,000, for the next 10 years. The competition, being run online until 31 March, will be backed by national press and online advertising and a direct drive using customer bills.
Npower, which is the official energy supplier to the stadium, first offered Wembley tickets as a prize in 2005, the year in which the stadium had been due to open. The ground is now expected to be ready in time for this year's FA Cup final, in May.
Npower will honour the prizes it has awarded in previous years, but will review whether to continue running the competition in future.
Rival utilities company E.ON is the official sponsor of the FA Cup, having signed a £32m four-year deal, so no Npower branding will be present at the first sporting event at Wembley.
When the E.ON deal was agreed in February last year, Npower marketing director Kevin Peake said he did not believe it would weaken its position, claiming that as E.ON and NPower's logos are similar, the two could easily be confused.
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