According to West Mercia police, the 48-year-old Atkinson was given medical treatment after being tasered but died around 90 minutes later.
An ambulance spokesman said while he was being taken to Princess Royal Hospital in the Shropshire town, his condition deteriorated and he suffered a cardiac arrest.
He was pronounced dead shortly after arriving at the medical facility.
The former striker is best remembered for scoring Villa's opening goal in their 1994 League Cup final win over Manchester United at Wembley.
He also won the first Premier League Goal of the Season prize for a fine individual effort for Villa against Wimbledon in the 1992-93 campaign.
Although he was never capped by England, Atkinson did play in one B international and scored his team's goal in a 4-1 defeat to the Republic of Ireland in Cork in 1990.
Atkinson's other clubs included Ipswich, Sheffield Wednesday, Real Sociedad, Fenerbahce and Manchester City.