Sauber, who currently use a year-old Ferrari power unit, said a new engine partner would be announced soon.
Honda, who risk having no team to supply next season if McLaren also decide to end their rocky relationship, said in a separate statement that its "strong commitment" to Formula One remained unchanged.
"It is very unfortunate that we have to discontinue the planned collaboration with Honda at this stage," said Sauber's new team principal Frederic Vasseur.
"However, this decision has been made for strategic reasons, and with the best intent for the future of the Sauber F1 Team in mind," added the Frenchman, who was boss of the Renault team until January.
"We would like to thank Honda for their collaboration, and wish them all the best for their future in Formula One."
Honda currently have an exclusive agreement with former champions McLaren, who are last in the championship after scoring two points in 10 races.
McLaren are also considering their options and the Sauber deal would have given Honda a continued presence in the sport, at worst, and two teams to work with on improving the power unit at best.
The Honda engine has been beset by reliability and performance problems, with McLaren's patience stretched to breaking point by the lack of straight line speed compared to rival teams.
Mercedes, Renault and Ferrari are the sport's other manufacturers.
Honda said Sauber, who are ninth out of 10 teams, had made the initial approach to them but the project had been called off due to "differences in the future direction between Honda and Sauber".
The partnership was agreed, but reportedly not fully completed despite being announced as a done deal, by former Sauber principal Monisha Kaltenborn.
The first female team boss, Indian-born Kaltenborn left Sauber in June.
"We had built a good relationship with Sauber, and had been looking forward to entering the 2018 F1 season together," said Masashi Yamamoto, general manager of Honda's Motor Sports division.
"However, during discussions after management changes at the team, we reached a mutual agreement to call-off the project due to differences in the future directions of both parties."
(Reporting by Alan Baldwin,; Editing by Ed Osmond)
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