Lord Hall is reported to have received a threatening email after dropping presenter Jeremy Clarkson from Top Gear because he had punched a producer.
The Mail on Sunday also reported Lord Hall and his wife were under 24-hour protection from security guards at their Oxfordshire home.
The Met said the email appeared to have been sent from outside the UK.
"Police in Westminster are investigating an allegation of threats to kill," a Met spokesman said.
"The allegation was reported to police on Wednesday, 25 March. The threat was made by email."
He said inquiries were continuing to establish from where the email was sent.
No arrests have been made.
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