Watson, who represented Team GB at the London 2012 Olympics last summer and is ranked 41st in the world, is unavailable for the tie as she continues her recovery from glandular fever.
Fellow Olympians Laura Robson, Anne Keothavong and Elena Baltacha as well as Johanna Konta make up the team with Britain ranked one place above Argentina in 16th in the Fed Cup rankings.
The winners of the tie in Buenos Aires will be promoted to 2014 World Group II and Watson, who was desperate to play, has vowed to support her teammates in any way possible.
"I am very disappointed not to be able to play Fed Cup. I was really looking forward to getting back with the team and competing against Argentina," said Watson.
"I will be following avidly and supporting the team from afar. It's a big miss for me and I will not only be missing the tennis but the team spirit and all the fun we have when we are together.
"I know the girls can win it and my thoughts will be with them."
- Sports & Recreation
- Anne Keothavong
- Johanna Konta
- Laura Robson