Salt, 28, flew home to the UK after Royal Challengers Bengaluru's (RCB) Qualifier 1 victory over Punjab Kings (PBKS) at New Chandigarh last Thursday to be with his partner over the weekend. Straight after the birth of their son, he flew back to India and landed in Ahmedabad in the early hours of Tuesday morning.
He played in the final later that night, hitting 16 off nine balls and taking an athletic catch in the deep as RCB beat PBKS to win their first-ever IPL title at the 18th time of asking. It was Salt's second consecutive IPL title, after his role in Kolkata Knight Riders' triumph last season.
Salt was singled out for his "unbelievable" commitment by Mo Bobat, RCB's director of cricket, after the final, while his opening partner Virat Kohli wrote on Instagram: "Now go back to the real stuff and get ready for changing diapers."
In the moments after RCB's victory, Salt said: "It's an unbelievable feeling right now. I'll be honest with you, I don't quite know where I am at the minute. I've not had the most sleep, but [I'm] so proud of the boys." Asked if the baby had brought him luck, he said: "He did. I've got a lucky charm now. I'm over the moon."
Salt was available for the IPL playoffs because England left him out of their ODI squad following a poor run of form earlier this year, including at the Champions Trophy in Pakistan. He was replaced at the top of the order by Jamie Smith, who will now take his place in the T20I squad for the series against West Indies.
An ECB statement said that Salt was "granted permission to withdraw" from the squad for the series, which starts on Friday in Durham. "Salt, who is taking time away on paternity leave following the birth of his child earlier this week, will now spend time at home," the statement added.
Salt's withdrawal may create an opportunity for Tom Banton during the T20I series after he was England's spare batter throughout their 3-0 ODI clean-sweep.