The Premier League side, fielding a different XI in each half, took the opportunity to give valuable run-outs to new signings Cheikhou Kouyate, Mauro Zarate, Diego Poyet and Aaron Cresswell at Portman Road but failed to find a way through, despite a handful of good chances.
Kouyate and Cresswell started the match - the latter given a warm reception on his return to the club from whom he joined West Ham on a five-year deal in the close-season.
The left-back looked bright early on, and he went close to making a decisive impact when his deft chip cannoned back off the woodwork after 14 minutes.
Mohamed Diame also saw a shot deflected just wide while, at the other end, Jack Marriott dragged a shot just past the post with Frank Nouble lurking.
With both sides using the break to make a raft of changes, the tempo dropped in the second half.
Zarate and Poyet were brought off the bench to boost the visitors' attacking options, but it was Sebastian Lletget who went closest to finding a winner for the Premier League side.
With 18 minutes left, the American attacking midfielder fired a left-footed effort goalward from 15 yards, but Ipswich goalkeeper Bartosz Bialkowski got a strong hand to the ball to make the save.
Zarate was withdrawn six minutes later to be replaced by Paul McCallum, with boss Sam Allardyce opting to ease his new Argentinian striker into English football following his move from Velez Sarsfield.
West Ham will next embark on a pre-season tour to New Zealand, taking in games against A-League teams Wellington Phoenix and Sydney FC.
