"The SANDF can confirm that the member received medical attention at the stadium and [was] released. The reports on social media platforms that the member is in the intensive care unit are not true," said spokesperson Brigadier General Mafi Mgobozi on Monday.
"The SANDF once again would like to caution the public not to spread incorrect and irresponsible information."
Mgobozi said the SANDF was concerned about the inaccurate reports being peddled around the incident.
Paratroopers were part of the major military displays during the swearing-in ceremony presided over by Chief Justice Mogoeng Mogoeng at the Loftus Versfeld Stadium.
The event was attended by thousands of South Africans and foreign delegates including several heads of state and government.
As he descended onto the pitch, directing his parachute, the soldier crashed into a soft-shell mortar launcher which was on display, sparking gasps from the terraces.
The video of the incident has been widely shared on social media platforms, particularly on Twitter and Facebook, and in many instances causing hot debates about the capabilities of the SANDF members.
Massive military displays and spectacular aircraft formations mesmerised the thousands of people who had come from different provinces and nations to witness Ramaphosa's inauguration.
African News Agency (ANA)