A spokeswoman for South Wales Police said the man has been arrested "on suspicion of displaying threatening abusive / insulting written material with intent / likely to stir up racial hatred. He is currently in police custody".
Comments by a 'Richard Gear Evans' on Facebook and Twitter read: "It's a shame that van was a nice drive as well".
The comments and account profiles for 'Richard Gear Evans' appear to have since been deleted, The Sun reported.
Father-of-four Darren Osborne was arrested by police after a van ploughed into pedestrians outside the Mosque on Seven Sisters Road in Finsbury Park, North London.
One person was killed and 11 others injured in the attack.