The 28-year-old has been hampered by the injury since joining from Liverpool last month.
He had been expected to make his full debut for the Viola this weekend against Catania, but the injury needs more time to heal than originally expected.
"ACF Fiorentina announces that Alberto Aquilani was visited today in London by Prof. Nicola Maffulli regarding his Achilles tendinopathy," read a statement on club's official website.
"The specialist found no significant changes, but suggested, however, treatment for another two weeks."
Aquilani has been capped 21 times by Italy at senior international level.