The RT-branded box contains food packaged in laboratory bottles, such as Medonium honey - "med" being honey in Russian and Meldonium a performance-enhancing drugs taken by athletes.
There is also raspberry jam tagged "anabolic" in reference to steroids also banned in sports.
"Not everyone realised this was a humorous present from RT," the broadcaster said. It has consistently denied and ridiculed allegations of a state-sponsored doping programme in Russia.
One of the gift boxes was sent to Yulia Efimova, who won two swimming silver medals at the 2016 Rio Olympics.
A photo posted on Russia's leading social networking website VKontakte shows a smiling Efimova with test tubes and vials apparently containing food, such as jam, honey and condiments.
On its website, RT gave further details of its gift pack which it suggested had also been sent to other people.
The website carried a video from the Twitter account of blogger Evgeny Kozlov showing one of the kits being unpacked.
People from RT are "unbelievably creative", he said.
The kits also include cards said to be based on drawings by children from an orphanage.
"A New Year's card that you will never throw away," said Yulia Ostroukhova, apparently another recipient of the gift box.
"Very nice. Many thanks for the delicious Medonium, too," she said on Facebook.
It is not clear how many kits were produced or how many recipients there were.
In July, an investigation commissioned by the World Anti-Doping Agency (Wada) said Russia's sports ministry "directed, controlled and oversaw" manipulation of urine samples provided by its athletes.
A number of Russian athletes were banned from competing at the Rio Olympics, but no blanket ban was imposed.
Another report later in the year alleged more than 1,000 Russians benefited from a doping cover-up between 2011 and 2015.
Russian officials have strongly denied there has been a state-sponsored doping programme.
BBC Monitoring reports and analyses news from TV, radio, web and print media around the world. You can follow BBC Monitoring on Twitter and Facebook.

Hampshire Police posted a photograph of a red car on its side, asking people to "retweet for a Hyundai i20 or FAV for a Vauxhall Corsa".
Some people called the tweet "inappropriate", but it was also described as "moronic".
"We were simply trying to show the impact of the crash. We didn't mean to offend," the @HantsPolRoads responded.
"Getting some negative replies to crashed car tweet.
"The driver was not injured in this incident. We were trying to highlight how much a car can be damaged in a crash."
No one was seriously injured in the crash on Wednesday on Redbridge Road, Southampton.
A number of people called the post "inappropriate", "irresponsible" and "making light of someone's traumatic experience."
Ian Taylor said: "Not inappropriate in the slightest. Absolutely moronic."
Alex Oates said: "A game out of a crash? What's next? 'did the driver/cyclist/pedestrian live? RT yes, FAV no?'."
Wayne Herridge said he had reported the post to Twitter as an inappropriate tweet.
A spokesman for Hampshire Police said two vehicles were involved in the collision and the driver of the red Hyundai had to be freed by Hampshire Fire and Rescue Service.
Nobody was seriously injured in the crash.
The Kremlin-funded international broadcaster RT, known as Russia Today, has produced New Year gift boxes branded "Russian doping".
[NEXT_CONCEPT]
People have attacked a tweet by a roads policing unit asking readers to identify the brand of a crashed car.