The former Australian cricketer has praised the exciting 20-year-old southpaw's ability to stay calm under pressure, reports bdnews24.com.
Bangladesh crashed out of the World Twenty20 after four successive Super 10s defeats.
Yet the young seamer, who joined the team in the second match of the round after recovering from an injury, snared nine wickets in three matches.
He bamboozled the New Zealand batsmen in their last match, returning 5/22 - the best figures of the 2016 edition.
"I met Mustafizur during the (T20) World Cup and he seems a good bright young kid. He will be looking forward to learning and to the opportunity," the official IPL website quoted Moody as saying on Thursday.
Mustafizur turned heads with his slowers and cutters since bursting into the scene in the ODI series against India last June.
The Sunrisers signed him up by outbidding Royal Challengers Bangalore during the IPL players auction on February 6 earlier this year.
"He has taken to big game cricket quite easily and we have already seen that in the World Cup stage and in the Asia Cup," Moody said.
"I feel he is more than comfortable and happy in big match situations. We have full confidence that he will adapt and adapt quickly," he added.
After Mustafizur flew to India on Tuesday, Bangladesh Cricket Board physio Bayezidul Islam has sent words of caution to his Sunrisers counterpart Theo Kapakoulakis.
"(The fitness of) every cricketer needs to be handled differently. In Mustafizur's case, we rest him after a couple of day's bowling," Islam said on Thursday.
"Sometimes he bowls a day and rests in the next. We have let him (Theo) know how much Mustafizur can take in the nets and the form of his physique in details," he added.