At 19 years and nearly four months, Toro Rosso's new recruit has only ever conducted two straight-line aerodynamic tests in F1 machinery.
But Alonso, who also debuted at the age of 19 for Minardi in 2001, insisted he does not have "any problem" with Alguersuari's rapid ascent.
"All the signs are that he is very good," the 2005 and 2006 world champion, who drives for Renault, is quoted as saying by the news agency EFE.
"If you are a formula one driver it is because you are good, so no one should worry," Alonso added, explaining that young drivers represent the sport's next generation.
"I am in favor of beginning as young as possible. I congratulate him and wish him a splendid future," he said.
In the same report, Alonso refused to comment on the ongoing speculation linking him with Ferrari.