"I took a bit of a knock but I'm happy to make it through the day and get to the finish line without losing any time to my main competitors," said the Briton who had an X-ray after the stage.
"The bumps and scrapes are fine but I fell heavily on my wrist so I needed to get it checked out by the doctors. I'm really pleased I've been cleared to race and I'm looking forward to getting back on the bike tomorrow.
"The wrist is painful and it's certainly not ideal going into tomorrow's cobbled stage but I have a great team around me and we'll get through the next few days as best we can."
Race doctor Florence Pommerie said Froome's wrist would need to be assessed again after Wednesday's leg, a 155.5km ride from Ypres to Arenberg Porte du Hainaut.
Froome fell off his bike five kilometres into the 163.5-km stage from Le Touquet but quickly got back in the saddle despite also bruising his hip, shoulder, knee and elbow.
The Briton, fifth overall and two seconds behind Italian Vincenzo Nibali, also crashed in last month's Criterium du Dauphine.
After Tuesday's incident he received treatment from Pommerie before being helped back into the peloton by his Sky team mates.
Dutchman Baike Mollema was also involved in the crash but seemed to escape unhurt.
Froome was also troubled by a back injury in March.
- Sports & Recreation