The TV presenter posted the one minute and 51 seconds video to Ms Sturgeon’s Twitter account, following the poisoning of a young white tailed eagle found dead in the Cairngorms National Park.
He said he and up to tens of thousands of people had written to the First Minister after the bird’s fate was revealed by police last week, but had become “impatient” at the lack of response.
In the video, which has been liked and retweeted thousands of times, he said such persecution of raptors in the 21st century “besmirches the reputation not just of the Cairngorms National Park but of Scotland and its landscapes generally”.
Mr Packham says: “Hello Nicola, Chris Packham here. Forgive this two minute intrusion and the impertinence but let me assure you that that impertinence has arisen due to impatience, and an impatience that’s not just mine but manifest by thousands, perhaps tens of thousands, of other people who have written to you within the last two weeks about the young white tailed eagle that was found earlier this year poisoned in the Cairngorms National Park. Frankly, we’ve had enough of it.
“You yourself commissioned a study into the fates of satellite tagged golden eagles and that review showed that within the National Park there were hotspots where, under suspicious circumstances, a significant number of these birds had disappeared.
“There have been a plethora of other wildlife crimes but this one is particularly hideous and it’s focused everyone’s ire on the continued criminal persecution of birds of prey in Scotland.
“So can I ask you please to firstly say something about this - either yourself or your erstwhile colleague (Environment Secretary) Roseanna Cunningham - and then secondly please do something about it. You are invested with that power.”
White tailed eagles - also known as sea eagles - are Scotland’s largest birds of prey, boasting an eight foot wingspan.
The species was wiped out in the UK when the last native bird was shot on Shetland in 1918. Reintroduced into Scotland in the 1970s, there are now more than 150 breeding pairs in Scotland.
Police Scotland appealed for information after the recent case referred to in Mr Packham’s video, in which the one year old eagle was recovered from a grouse moor in Donside, Aberdeenshire, in April.