A Hampshire police spokeswoman said: “At 11.50am on July 22, we received a report of a letter containing threats to kill a Portsmouth woman and her family which was sent to her office in Lakeside, North Harbour.
“We attended and safeguarding measures were put in place to minimise the risk to the woman and her family, employees and the wider community.
“Our inquiries into this incident are ongoing and it has been referred to the Parliamentary Liaison Team.
“We take the safeguarding of our MPs incredibly seriously and there are robust systems in place to ensure they can carry out their job safely.”
It is believed negative press reports and the heightened public profile of Ms Mordaunt during her leadership bid sparked the death threat before she was voted out of the contest on Wednesday.
Ms Mordaunt added: “I’m very grateful to the police for their swift action.”
Donna Jones, police and crime commissioner for Hampshire – who supported Ms Mordaunt’s campaign to be Tory leader – said she was appalled by the new threats.
She said: “The threats both online and in person towards public figures are growing and getting worse.
“The death of Jo Cox and Sir David Amess reminds us that often these violent attacks are linked to people who are suffering with mental health issues.
“The threats made to Penny Mordaunt are deeply worrying and it’s right that Hampshire Constabulary looks into the threat fully.”