Warner was on Sunday ruled out of the remainder of the ongoing triangular One-Day International (ODI) series in the West Indies due to a broken finger, which he suffered while fielding during the match against South Africa here on Saturday. The series also includes the hosts as the third team.
"I think he is out for the tri-series so the most important thing from my aspect is that he is right for the Test series (in Sri Lanka)," Smith told cricket.com.au.
"I think that's about six weeks away and the medical staff and Dave are confident he will be fine for that first Test match."
Smith said it was tough to miss the swashbuckling opener, who was named Man of the Match on Saturday for his first ODI century outside Australia at the Warner Park.
"It's tough missing guys like Dave. He's in the form of his life and batting beautifully and he will be a big loss for us. He has played beautifully at the top of the order on some difficult batting wickets. They have been quite slow ... so far throughout the series," he said.
"It's about adapting and getting yourself in. It might take a little bit longer than normal but once you have got yourself in you have to cash in because it's difficult for the new batsman."
Warner, who recently led the Sunrisers Hyderabad to their maiden Indian Premier League (IPL) crown, said the break will provide him spend quality time with his family.
"It's obviously disappointing to be sidelined given the form I've been in," Warner said in a statement.
"(But this) will give me the chance to freshen up and spend quality time with my family after an intense period of action."
Australia will take on the West Indies here on Monday with the final on June 26.
The Kangaroos will then travel to Sri Lanka for the three-match Test rubber, starting on July 26 which also includes five ODIs.