The tweet mocked columnist Toby Young's contribution to the programme. It was later deleted.
Police Scotland said the matter was being investigated and Twitter access was being reviewed.
Mr Young said he had blocked the force's account, was not offended and would not complain.
The journalist was appearing in a discussion with Labour MP Stella Creasy.
Ms Creasy, who has received threats of rape on Twitter, wants social networks to do more to protect users and to identify perpetrators.
This debate over internet abuse – known as “trolling” – began when Caroline Criado-Perez was bombarded with abuse via Twitter after successfully campaigning to have author Jane Austen depicted on the new £10 note.
Ms Creasy appeared on Newsnight with Mr Young on Tuesday night.
The MP told the programme: “We need to make sure that police at a local level and at a national level understand the risks and dangers that can come from online behaviour.”
Mr Young, who writes for the Daily Telegraph, argues that blocking and ignoring abusive posters on the internet is sufficient “in 99 cases out of 100”.
After receiving the message from the Police Scotland account, Mr Young [@toadmeister] tweeted: “Just had to block @policescotland, the official police Scotland twitter feed, for abusing me on twitter. This is getting weird”
On Wednesday morning, Police Scotland tweeted: “We apologise for the tweet sent to @toadmeister & for any upset caused. The matter is being investigated & we're reviewing Twitter access.”