The sender of the letter, sent to her Portsmouth North constituency office, threatened to “shoot her in the head” and “kill her family”.
“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,” a Hampshire police spokeswoman said.
“We attended and safeguarding measures were put in place to minimise the risk to the woman and her family, employees and the wider community.”
The spokeswoman said police inquiries into the incident are ongoing and that the case 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,” she added.
Ms Mordaunt's office has been approached for comment.
A former Royal Navy reservist, Ms Mordaunt said during her campaign that the UK’s leadership “needs to become a little less about the leader and a lot more about the ship”.
She was never a front-runner among MPs but some of them fear her departure from the race lessens the chances of them holding on to power at the next election.
Of the final three candidates, she had the most popular appeal among both Tory membership and the wider population.
The field has been whittled down to Rishi Sunak and Liz Truss, who will first make their cases to party members over the next six weeks and then to the British public when one of them is announced as prime minister on September 5.
Before entering Parliament, Ms Mordaunt worked in communications in the UK and the US, and played a role in the presidential campaign of George W Bush as head of foreign press.
She first stood for election in 2005 in Portsmouth, and while she was unsuccessful, she gained redemption five years later in 2010, winning the seat for David Cameron's Tories.
Ms Mordaunt has held a variety of ministerial positions and two Cabinet roles: former prime minister Theresa May appointed her secretary of state for international development in 2017 and then in 2019, after the sacking of Gavin Williamson, she was elevated to defence secretary — a position she held for only 85 days, with Boris Johnson firing her after he became prime minister.