Rose, 26, was replaced by Ben Davies during Tuesday's 0-0 draw at Sunderland and had a knee scan on Thursday.
The England international has started 18 of Spurs' 23 Premier League games this season, but will miss the visit of Middlesbrough on Saturday.
"We need to wait until Monday to see the specialist," said Pochettino.
The Argentine is also without defenders Kieran Trippier and Jan Vertonghen, who suffered an ankle ligament injury two weeks ago.
"Jan Vertonghen is better and starting to run, which is very positive," added Pochettino.
Tottenham left-back Danny Rose will see a specialist on Monday to confirm the extent of his knee injury, manager Mauricio Pochettino has confirmed.