Riggott, who signed from Derby on January 31, limped out of Saturday's 1-1 draw with Everton at half-time.
Boro have limited cover in central defence because impressive 18-year-old Andrew Davies is suffering from mumps.
Fortunately, Ugo Ehiogu is approaching full fitness after overcoming broken ribs and a punctured lung on New Year's Day, and veteran defender Colin Cooper is in tremendous nick.
Riggott's injury could force Steve McClaren to recall Jason Gavin from Sheffield United as cover.
The out-of-favour Irish defender is on trial at Bramall Lane for one-week.
Meanwhile, Newcastle midfielder Gary Speed today said Boro would find Middlesbrough-born Jonathan Woodgate a rock in defence in tomorrow's Tees Tyne derby.
Speed reckons Woodgate has settled into the Magpies' line-up like a dream.
The £9m central defender enjoyed a superb debut in Saturday's victory against Chelsea at St James' Park. Now the 23-year-old is set to make his first away start.
Speed said: "You could tell Woody was quality as soon as he arrived at the club but sometimes it takes players a few games to settle into a side. But Woody slotted in straight away."