CA physiotherapist Alex Kountouris said the decision to send Hayden home was made to ensure his fitness during Australia's upcoming international schedule.
"Matthew Hayden's right Achilles' tendon injury has not made sufficient progress during his time in the West Indies and as such he will not be able to participate in the second Test and was highly unlikely to be available for the third Test," Kountouris said in a statement.
"With the large volume of cricket to be played over the next 18 months it was decided he should return to Australia to undergo rehabilitation and consult specialists."
Cricket Australia chairman of selectors Andrew Hilditch said Hayden's departure was a disappointment for the batsman but presented an opportunity to his replacement Brad Hodge.
"It means that Brad Hodge will remain with the side which is richly deserved given his strong performance in the first Test," he said.