The teenager was held and questioned on suspicion of racial abuse after the posting of a message on Twitter after Welbeck scored the winner to knock his former club Manchester United out of the FA Cup on 9 March.
A Wiltshire Police spokesman said: "A 15-year-old male from the Salisbury area was arrested on the evening of March 12 on suspicion of racial abuse.
"He has been released on police bail until April 13. The investigation is ongoing."
Welbeck, who has been capped by England 32 times and scored 12 goals, joined Arsenal for $31.11 million last year after the arrival of new Manchester United boss Louis van Gaal.
The Manchester-born striker spent six seasons at Old Trafford after coming through the club's youth system.
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