The paper manufacturer, which acquired M-real's coated graphic paper business in November, will take out between 40,000 and 60,000 tonnes of capacity in Europe.
Andre Oberholzer, Sappi's group head of corporate affairs, said the reasons behind the curtailment were a slowdown in market demand due to depressed economic conditions and an insufficient reduction in input costs.
He said: "Input costs are well above 2007 averages, and we believe the market will remain depressed. However, we are hopeful that input costs will reduce over the next year."
Sappi said that it hoped to stimulate demand by promoting the advantages of paper-based communications.
Oberholzer said: "This must always remain in focus, along with achieving acceptable pricing levels, reducing input costs and closing uncompetitive capacity."
Earlier this month, the paper manufacturer announced that it will increase the price of its coated fine and mechanical coated grade papers by 8 to 10% as of 1 January 2009.
As a result of Sappi's €750m (£596m) acquisition of M-real's coated graphic paper business, the company has expanded its woodfree coated products. Its European graphic paper capacity has been increased from 2.6m tonnes per annum to 4.5m tonnes per annum.
Sappi has warned that key challenges for 2009 include continued pressure from input costs, lower market demand and currency fluctuations.
Oberholzer said: "We also believe that further consolidation within the sector will be of benefit to the industry and customers alike."
Sappi to rein in fine paper output by a fifth
Sappi Fine Paper Europe has said it will curtail its fine paper production in the coming months by "at least 20%", as a result of continuous adverse market conditions.