Football Kenya Federation (FKF) said 61-year-old Put, who took charge of the Harambee Stars in November and led the team to win the CECAFA Challenge Cup the following month, had resigned for personal reasons.
"The tactician's resignation, though down to personal reasons is a setback to the country's ongoing 2019 Africa Cup of Nations qualifiers, as he was an integral member of the technical bench," FKF director of communications Barry Otieno said.
Early this month, Put had called for a more technical approach to the management of the national team in a bid to qualify for the continental tournament's finals in Cameroon.
Kenya is currently placed third in Group F after a 2-1 loss away to Sierra Leone in the opening match last June, and is scheduled to play leaders Ghana in their second match in Nairobi on September 7.
Former head coach Stanley Okumbi, who deputised as Put's assistant, is expected to continue training the team on an interim basis as Kenya looks for Put's replacement.