Liden School children were told to stay inside over lunchtime whilst armed police carried out a raid in Barrington Close.
Residents were also told to stay inside or not to return home whilst the operation was carried out around midday.
The operation, which occurred without incident, was carried out after a domestic incident at an address in Park North last night.
Armed police were used due to concerns the suspect may have access to a weapon and officers have revealed that they will be carrying out further arrest attempts at various other addresses across the town today but that the public should not be concerned.
A Wiltshire Police spokesman said: "Following a domestic incident at an address in Park North overnight, police have been carrying out arrest attempts at various addresses across Swindon.
"Nobody was injured during the domestic incident, but due to concerns that the suspect may have access to a weapon, armed police have been deployed to carry out the arrest attempts.
"People may see an increased police presence in parts of the town, but should not be concerned."