Hendrix's contract, which the musician had signed, is expected to fetch up to $250,000 (£151,287).
The tapes, recorded by Madonna in 1992 and 1993, have been estimated to sell for up to $40,000 (£24,205).
Items once belonging to John Lennon and Elvis Presley are also lots in the auction, which runs until 5 August.
The two Madonna cassette tapes each hold 17 minutes of material.
The messages recorded by the singer were left for James Albright, the bodyguard who eventually became her lover.
An intimate home video featuring Madonna, which she also sent him, has an estimated value of up to $14,000 (£8,461).
The Gotta Have It! auction house, based in New York, described the video as 'very personal and intimate', but refused to say exactly what was on it.
From BBC News