He injured himself while climbing in the Scottish Highlands last Wednesday.
Mr Smith, 55, was due to visit a farm at Beccles, Suffolk, today, followed by a news conference in Lowestoft and meetings in Great Yarmouth and Ipswich. He will be unable to attend the House of Commons this week.
In 1988, Mr Smith suffered a heart attack from which he appears to have made a complete recovery. Since his illness, he has taken to climbing - particularly the mountains higher than 3,000ft, the Munros.
He slipped in the snow while climbing his 108th Munro, Eididh nan Clach Geala, in Wester Ross.
A spokeswoman said: 'After he did it he continued to walk three or four miles further on. And on Friday, not realising the damage that had been done, he carried out a number of engagements in his constituency.'