The Italian, who won last month's Fifa elections to succeed Sepp Blatter, inaugurated the facility in the war-torn country's capital Juba.
He also attended the 2017 Africa Cup of Nations qualifier between South Sudan and Benin, which the away side won 2-1.
South Sudan played their first official friendly, against Uganda, in July 2012.
It was only in 2011 that organised football was first played in South Sudan, after the country gained its independence from Sudan.
South Sudan officials dressed Infantino in traditional robes and made him dance. Officials also produced a large cake to celebrate the Italian's 46th birthday.
After gaining independence from Sudan in 2011, South Sudan erupted into civil war in December 2013.
Infantino, who won last month's Fifa elections to succeed Sepp Blatter, is due to visit South American football confederation CONMEBOL from 28 to 29 March in Asuncion, the capital of Paraguay.

The London Taxi Company's (LTC) Ansty Park site in Coventry is the home of its new electric taxi, the TX5.
LTC - which now employs up to 1,500 people - has invested more than £300m in the TX5 after manufacturing the black cab in the UK for 69 years.
Administrators were called into LTC in 2012 before Chinese carmaker Geely bought the business the following year.
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The first electric taxis to roll off the production line will go on sale in London in the final quarter of the year, before being sold around the world early in 2018.
It has been described as one of the great comeback stories in UK manufacturing history - and that is exactly what it is.
Back in 2013 London Taxis International was on its knees and looking for a new owner.
Then Chinese firm Geely came to the rescue and almost immediately announced plans to build a new factory - but not only that, it revealed plans to make electric vehicles and employ more than 1,000 people.
It is the first all-new car factory in the Midlands since 2003, when Aston Martin opened its state-of-the-art plant at Gaydon in Warwickshire. That was on a much smaller scale, though.
It is also one of the biggest single Chinese investments in the region and it shows that the West Midlands continues to lead the way when it comes to both automotive research and development and production.
LTC, previously known as LTI, started life in the 1920s, producing car bodies for Jaguar, Rolls Royce and Bentley.
It will retain its existing Holyhead Road premises in Coventry as a paint shop once the production of the existing TX4 taxi ends in the summer.
Staff have moved into the Ansty Park plant this month ahead of Wednesday's official lunchtime opening, involving company representatives.
The new site will house a research and development centre for the electric vehicle, with engineers accounting for 200 of the newly-created jobs.

The 25-year-old forward has been signed for the second half of the Womens Super League season, which will resume for Blues on 29 June at home to Arsenal.
"It further outlines our intentions and vision of what we want to achieve at the club," said manager David Parker.
Blues fought off competition from some major European sides to sign Linden.
"It's a signal of the development the club is making not just in England but also in Europe that we are now attracting the top European players," added Parker.
She is the third German to join this season following the signing of Corina Schroder from Liverpool and the arrival in April of defender Marisa Ewers from Bayer Leverkusen.
On the back of two wins in three matches, Blues have climbed to third in WSL 1, seven points behind leaders Manchester City.
Linden said: "The conversations with David, (assistant manager) Marcus Bignot and (chief executive) Tim Andrews convinced me about the project and ambitions at the club.
"I'm looking forward to the new challenge to play in another country. I have always wanted to play in England."
Linden, who played at SGS Essen and Bayer Leverkusen before joining Frankfurt for the 2015-16 season, has represented Germany at every level.
South Sudan Football Association's new office was opened by new Fifa president Gianni Infantino on Wednesday.
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A £300m taxi manufacturing plant which created 1,000 new jobs is to be officially opened later.
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Birmingham City Ladies have signed Germany international Isabelle Linden from Champions League holders FFC Frankfurt.