Hampshire Police were notified about the threats, which were made by telephone and prompted teachers to evacuate their pupils.
Similar calls were made to schools across the country on Wednesday and a number were evacuated, including Boxgrove Primary School in Guildford.
The Hampshire schools affected were Oakfield Primary School in Totton, Castle Primary School in Portchester and Castle Hill Primary School in Basingstoke, which received calls between 9am and 9.30am.
All three schools took the decision to evacuate pupils and staff, before searches were carried out by police. They returned to their schools by 11.30am.
A Hampshire Police spokesman said: "At this time, it is believed the threats were a malicious hoax and there is no direct risk to pupils, staff or the wider community.
"We take hoaxes extremely seriously. They divert police resources and cause disruption and alarm to the public."