The Argentine joined Saints from Racing Club in January 2023 but could not help them avoid relegation despite scoring four times in 18 Premier League games.
However, the 21-year-old midfielder has managed only three goals in 23 Championship games this season.
"It's an amazing opportunity for him to go and play for a huge club with huge history," said Martin.
Alcaraz - known as Charly - has only completed 90 minutes three times in the league this season and has played 14 minutes in the two Championship matches since the turn of the year.
Serie A giants Juventus will reportedly have an option to buy Alcaraz for around £40m in the summer.
"He's a player who's probably been a bit frustrated with the minutes he's played recently," Martin told BBC Radio Solent.
"We signed Joe Rothwell early and have Joe Aribo coming back. We were really aware of interest in Charly from a few clubs in January.
"If he had stayed, no problem, but he's ended up going. I think it suits everyone, I think Charly wants to play more and he has the chance to go and make an impression at a huge football club."
Director of football Jason Wilcox added: "Juventus are a huge club and we are convinced that this move will allow Charly the opportunity to flourish and then come back and be a success at Southampton."