Totti had hoped to make a rapid recovery in time to face arch-rivals Lazio this weekend.
He limped off during the 3-1 win over Atalanta clutching the back of his right thigh and today's test results were not reassuring.
"After the tests performed this morning at Trigoria, Totti continues his rehabilitative work of physiotherapy and pool exercises," read a statement.
"Over the next few days he will begin working in the gym. Another test to evaluate the course of the injury is expected next week."