Silva's elder sister Nelum Anusha Silva and Tennakoon's father P B Tennakoon died early today, Sri Lanka media manager Brian Thomas said.
The two families were not related and the deaths were due to illnesses.
Funeral arrangements have yet to be announced and it was not immediately known if Silva, a key middle-order batsman, will feature in the co-host's World Cup opener in Group A against Canada in the southern Hambantota district on Sunday.
Thomas said the team was concentraing on its cricket despite the events.
"The boys are focussed on the World Cup, they really feel sorry for their colleague's sister and father of their manager," Thomas said.
"These are difficult times, they are one family. They are rallied together."
Co-hosts India and Bangladesh will meet in the tournament opener on Saturday in Dhaka.