Police said the man, whose name was not released, remained in police custody.
Johnson, 29, suffered a fatal injury when his neck was cut by the blade of another player during the match against Sheffield Steelers in Sheffield, northern England.
The American, who joined the club in August having previously played in Germany and Sweden as well as in the United States' National Hockey League (NHL), later died in hospital.
"Our investigation launched immediately following this tragedy and we have been carrying out extensive enquiries ever since to piece together the events which led to the loss of Adam in these unprecedented circumstances," Detective Chief Superintendent Becs Horsfall said.
The coroner overseeing the inquest has called for neck guards to be made mandatory in the wake of the death, which Johnson's club described as a "freak incident".
"Adam's death has sent shockwaves through many communities, from our local residents here in Sheffield to ice hockey fans across the world," Horsfall said.
The NHL said they had no comment on the development related to the arrest.
Nottingham Panthers will host an "Adam Johnson Memorial Game” on Nov. 18 when members of the team will wear a specially commissioned "AJ47" memorial jersey.
The club also paid tribute to Johnson by painting a message on the ice at their home ground reading: "Adam Johnson Forever our 47".
