The 37-year-old is the lead throws coach at Loughborough University and has a part-time contract with British Athletics, where he works under the national governing body's throws and jumps coach Peter Stanley.
The relationship is understood to have taken place with an athlete at the university.
In a statement, British Athletics said: "British Athletics and Loughborough University can confirm that a coach has been suspended pending an investigation.
"Both organisations are working closely to support any athlete who may be impacted in any way."
Parker, the world junior javelin champion in 1998, was the British team leader at the European U23 Championship in Poland this summer.