While some Twitter and Instagram users have made the profile picture circle appear solid blue, others posted a solid blue square as an image. Some have done both.
Instagram has so far recorded close to 18,000 posts with the hashtag #BlueForSudan.
"It is time to stand hand in hand. Their voices must be heard. #BlueForSudan," wrote one Twitter user.
"Ignorance is worse than violence.. Stand with Humanity, Stand with #sudan #BlueForSudan," wrote another.
Some users have also posted the drawing of a crying woman wearing a hijab to draw attention to the political crisis in the north African country.
The violence in Sudan followed a couple of months after the ouster of long-running President Omar al-Bashir on April 11.
The trigger for social media users to turn blue was the death of a young man who was allegedly killed during a crackdown on protesters on June 3.
"Those who are taking part in spreading #BlueForSudan. The colour blue came from a warm hearted, martyr known as, Mohammed Hashim Mattar, my cousin who has passed away on the 3rd of June, as he was standing proud. Blue was his fav colour, which now presents unity. Mattar's Blue," tweeted one user.
To honour his death, Mattar's friends and family put up the blue colour on their profiles, but others soon followed.
The Sudanese government last Thursday said that 46 people were killed in "recent events" that began with an assault on a protest camp earlier this week in the capital Khartoum, while the opposition Committee of Doctors said at least 108 people had died.
In what was the first official death toll since a military crackdown on a camp that had been set up for two months, the Sudanese Undersecretary for the Health Ministry, Suleiman Abdul Jabbar, said in a statement that the toll had not reached 100, Efe news reported.
Sudanese security forces last Monday raided an encampment that had been set up in front of the Army headquarters since April 6 and began firing to clear the area.
The Army cracked down on the demonstrators and destroyed the encampment, the nerve centre of the protest that led to the overthrow of long-running President Omar al-Bashir on April 11.
( With inputs from IANS )