The match was due to take place on Saturday, but a number of Shrewsbury players and staff members have tested positive for Covid-19.
The Football Association’s Professional Game Board will meet early next week to decide what will happen to the fixture.
A statement on Southampton’s website read: “Southampton’s FA Cup third-round game at home to Shrewsbury Town will not take place as scheduled this Saturday.
“The club received notice of the decision from the Football Association this morning, after a number of Shrewsbury players and staff members tested positive for Covid-19.”
Shrewsbury said they had “reluctantly” advised the FA they would be unable to fulfil the fixture after medical advice said it would be unsafe for the game to take place.
The League One club have been unable to train since last week and have closed their Sundorne Castle training ground for 10 days.
Rachel Robinson, Shropshire’s director of public health, said in a statement on the club’s official website: “We have been made aware of positive cases of Covid-19 at Shrewsbury Town Football Club.
“We are working closely with the club to help limit any further potential spread. All positive cases, as well as close contacts, are self-isolating for at least 10 days in line with national guidance.
“The club has acted responsibly and taken all the necessary precautions to limit the spread of the virus, which in this case has required closing the training ground and isolating all close contacts.
“The club are also following all the Government’s elite sport protocols, which include regularly testing players and staff.”
Southampton had their own concerns last week after goalkeeper Alex McCarthy tested positive for coronavirus and had to miss his side’s win over Liverpool.
Shrewsbury’s statement added: “The health and safety of all staff members at Shrewsbury Town Football Club remains paramount and the club continually takes all necessary steps to protect all where possible.”
Elsewhere, both Aston Villa and Middlesbrough have seen their preparations for their third-round ties disrupted by a series of positive tests.
Villa, who are due to host Premier League counterparts Liverpool on Friday evening, have closed their Bodymoor Heath training ground after revealing “a large number” of players and staff members had contracted the virus.
A statement issued on Thursday afternoon read: “Aston Villa can confirm that the Club has closed its Bodymoor Heath training ground after a significant Coronavirus outbreak.
“A large number of first team players and staff returned positive tests after being routinely tested on Monday and immediately went into isolation.
“A second round of testing was carried out immediately and produced more positive results today.
“First team training ahead of tomorrow’s FA Cup match with Liverpool was cancelled.
“Discussions are ongoing between medical representatives of the Club, the Football Association and the Premier League.”
Villa’s announcement came hours after Boro, who travel to Brentford on Saturday, confirmed positive tests.
The Sky Bet Championship club, whose manager Neil Warnock tested positive last year, effectively shut down their Rockliffe Park training headquarters on Monday after cases among first-team staff and players had been confirmed, and a further round of testing, which also included under-23s players, took place on Thursday morning with the results expected before the weekend.
Derby chief executive Stephen Pearce confirmed on Wednesday that the club will send a group of under-23 and under-18 players to play in the FA Cup at Chorley on Saturday following a coronavirus outbreak which has closed their training ground.
Wayne Rooney and Derby’s entire first-team squad will miss the third-round tie in Lancashire, with Pearce revealing nine players and staff within that bubble have tested positive for Covid-19.
Meanwhile, Manchester City confirmed their Women’s Super League game against West Ham this weekend has been postponed due to positive coronavirus tests at the club.
City were scheduled to play West Ham at home on Saturday, but after four players or staff members tested positive the game has been called off, the club said.