Yes, this is quite common, especially in smaller countries. Some examples:
In 2017, the President of Panama declared a one-off public holiday after their national football team qualified for the World Cup for the first time. This was then replicated in Peru later that year, and was also the case in Trinidad & Tobago in 2005.
Colombia had a half-day public holiday in 2014 after beating Uruguay to reach the quarterfinals of the World Cup, so that public employees could watch the match.
Similarly, in 2018, the Maldives declared a public holiday after their national football team’s success in the SAFF Cup.
For Olympic success - @Panda has mentioned Fiji & Bermuda’s national holidays for their Rugby Sevens team and for the triathlete Flora Duffy respectively - similarly, in Grenada, a half-day holiday was held to celebrate Kirani James’ success in the 400m in 2012. Again in Trinidad & Tobago, a public holiday was declared in 2012 after their team’s success - especially that of Keshorn Walcott’s gold medal in the men’s javelin.
Also in Malaysia, the Prime Minister announced a public holiday after the medal target was surpassed in the 29th SEA Games.