A 34-year-old man from Huntingdon has been arrested on suspicion of exposure; he remains in custody.
Police have withdrawn an e-fit image of a man they would like to speak to in connection with the alleged incident.
At about 8.10am on Monday, 9 January, three young children were walking along the footpath behind Percy Green Place, in Stukeley Meadows, when it is claimed a man exposed himself to them.
PC Matthew Smith said: “This incident saw three children left shocked and distressed.”