The game - at Wembley on April 18 - will be used by the government as the first football test event as part of the phased return of fans to stadiums.
It will be followed by the Carabao Cup final between Tottenham and Manchester City on April 25 - which will have a larger yet still limited number of supporters in attendance.
Tickets will be restricted to Brent Council staff, Brent and NWL NHS and care staff, local school teachers and pupils over 18, Wembley Park residents and business and the local voluntary sector.
Those eligible for tickets can register there interest on the Brent Council website here.
Clubs cautiously began to welcome back fans towards the end of last year before the infection rate spiked alarmingly across the country, prompting a dramatic U-turn and shift in government policy.
Now, though, with lockdown restrictions being eased, steps are being taken to bring crowds back into sporting arenas - and Leicester vs Southampton will represent the largest crowd since the pandemic began.
The FA Cup semi-final is set to be one of 14 pilot events to be announced by the government, which will also include the Carabao Cup final and the FA Cup final.
Culture Secretary Oliver Dowden, speaking recently, said: "These test events will be crucial in finding ways to get fans and audiences back in safely without social distancing.
"We will be guided by the science and medical experts, but will work flat out to make that happen.
"We want to get the people back to enjoying what they love and ensure some of our most important growth industries get back on their feet."
The FA are yet to announce their plans for Euro 2020, with Wembley set to host more games than any other stadium, including both semi-finals and the final.
UEFA still plan on staging the tournament across 12 countries despite widespread restrictions on socialising in Europe and are yet to confirm whether or not fans can attend.
It is understood the FA are hopeful of hosting 45,000 people for the semi-finals and the final, depending on how the pilot events go this month.
The FA Cup semi-final between Leicester and Southampton will be played in front of 4,000 spectators as one of a number of pilot events starting this month.