Samoa Global News reports that Leilua was informed his daughter, born on 3 November, had been admitted to Isolation 2 at Motootua National Hospital shortly after arriving in Dubai last week.
The 23-year-old, who has scored 20 tries in 69 appearances on the World Sevens Series, told the website that there has since been "improvement" and that he is praying "for all the families affected by the measles".
Paulo Fanuasa and Kelvin Masoe have been called into the Samoan squad in Dubai and head coach Sir Gordon Tietjens said the whole team was thinking of Leilua and his family.