The 38 year old was speaking ahead of Friday's ceremony at the Maracana Stadium.
She added that she was "filled with joy and excitement" to have the opportunity to carry the Swedish flag.
It will be her sixth Olympics, which is a record for a female swimmer.
Alshammar is one of the Swedish athletes who has experienced success before, winning two silver medals and a bronze at the Sydney Games in 2000.
Fellow swimmer Sarah Sjöström is Sweden's big medal hope this time around. She races for the first time this weekend.
Other flag bearers in Friday's athletes' parade include Michael Phelps, the 18-time gold medal winner who is carrying the US flag, and tennis player Andy Murray carrying Great Britain’s.
Show jumper Rolf-Göran Bengtsson carried the Swedish flag at the 2012 Games in London.
Updates on the Olympics will be available from Radio Sweden starting Monday morning (Swedish time).