New Zealand Cricket were unable to provide immediate comment but had called a press conference early on Friday.
Taylor's sacking comes in the wake of local media reports of disharmony between the 28-year-old batsman and head coach Mike Hesson.
Taylor scored 142 and 74 in his last two innings as he led from the front to guide New Zealand to a rare away test win over Sri Lanka in Colombo that tied their series 1-1.
McCullum faces a baptism of fire with upcoming series against South Africa and England. (Writing by Ian Ransom; Editing by Nick Mulvenney)