Ms Conway is seen clutching her phone as US President Donald Trump poses with leaders of historically black colleges and universities.
Twitter users accused her of "disrespect".
Ms Conway was taking her own photos at the time.
"That's no way to act in the People's Oval Office," tweeted one user of the social media site.
"Think of all the great people who sat on that couch and put your feet down," wrote another.
The images led some to question Ms Conway's body language, suggesting that she was not taking the meeting on Monday seriously.
Others downplayed the excitement, indicating that it was all a bit of a storm in a teacup.
The images of Ms Conway also drew comparisons to a photograph taken in 2013 showing then President Barack Obama with a foot up on the Oval Office desk.
"What a story. Hope Obama never put his feet up on the furniture," writes Kevin.
Mr Trump was meeting leaders of historically black colleges and universities to discuss his administration's support for the schools, including contracts and grants.
Ms Conway is no stranger to controversy. Earlier this month she was criticised after citing a "massacre" which never happened while defending Mr Trump's controversial immigration ban.
Her recent promotion of products linked to Mr Trump's daughter, Ivanka, led to calls for an investigation into whether she had violated ethics rules.

The largest dinosaur on show at Wollaton Hall in Nottingham will be the 23m (75ft) Mamenchisaurus, which will be displayed "rearing up on its legs".
The massive plant eater would not fit into the hall at full length.
In 2011 the museum closed for several days to allow filming for the Batman movie The Dark Knight Rises.
The museum will reopen on 30 June for the launch of the exhibition.
Curator Adam Smith said: "The collection will tell the story of how dinosaurs evolved into the birds and will feature some of the biggest dinosaur skeletons in existence."
The fossils, which arrived on Friday after a 50-day journey, will be erected by a team of six specially-trained technicians.
The Mamenchisaurus, a planting-eating sauropod similar to a brontosaurus, was found in Sichuan Province in south west China in the 1970s.
Some of the 23 exhibits, including the Gigantorapror, a birdlike dinosaur with a toothless beak, are considered "national treasures" in China.
The museum and the University of Nottingham have been working with Chinese authorities since 2011 to bring the exhibition to the UK.
Once open, the show will run until 29 October.

The 19-year-old defender, who has made four appearances for the Tractor Boys this season, will remain at Portman Road until the summer of 2019.
The deal includes an option for the academy graduate to extend his stay by a further year, until 2020.
"I'm enjoying my football and I want to keep on improving my game," he told the club website.

Allan Bryant, 23, went missing after a night out at Styx nightclub in his home town of Glenrothes on 3 November 2013.
Officers began searching the house in Barnton Place on Friday 16 June.
Police Scotland said the property had now been returned to its owners and no further investigations would be made at the house.
Det Insp Stuart Wilson, of Police Scotland, said: "Inquiries into the circumstances of Allan's disappearance are ongoing and we are committed to finding him.
"We still believe that someone in the Glenrothes area has information that will assist with our inquiries.
"I would ask that person to come forward and help us give the Bryant family the answers they are desperately seeking."
Mr Bryant's parents have repeatedly stated they believe he has been murdered and that his killer is still at large.

3 March 2017 Last updated at 14:07 GMT
Romeo, aged four, asked his father Charlie Makaveli if he could go to school dressed as the leader of the Autobots, Optimus Prime.
It took his father a week to construct the outfit out of cardboard, paint and glue.
Mr Makaveli, a florist from Romford, east London, said his son got a big cheer when he showed how his outfit "transformed".
So far, the video has been viewed about 50,000 times on Mr Makaveli's Facebook page.
Senior White House adviser Kellyanne Conway has sparked a social media storm after pictures emerged of her kneeling on the sofa in the Oval Office with her shoes on.
[NEXT_CONCEPT]
A natural history museum has closed to allow a "massive" exhibit of dinosaurs from China to be erected.
[NEXT_CONCEPT]
Ipswich Town youngster Josh Emmanuel has signed a new contract with the Championship club.
[NEXT_CONCEPT]
Police investigating the disappearance of a Fife man have ended the search of a house in Glenrothes without making any fresh discoveries.
[NEXT_CONCEPT]
A father really went to town when his son asked for a Transformers outfit for World Book Day.