The January RBC PMI reading was 51.7 on a seasonally adjusted basis, down from 53.5 in December.
The index is intended as an indicator of trends in the manufacturing sector. A reading above 50 indicates expansion.
All five of the index components fell in January from December, but the bank noted the decline was smaller than between November and December, when the index dropped two full points.
"Underlying economic conditions — such as stronger growth in the U.S. economy and a weaker Canadian dollar — remain supportive for the outlook for domestic manufacturing in the period ahead," said Craig Wright, RBC's chief economist.
But the bank said January showed the slowest improvement in business conditions since April 2013. It also indicated production levels grew for the ninth month in a row, but the increase was the smallest since August.
The index is compiled in co-operation with the Supply Chain Management Association and Markit, a financial information company that compiles similar indexes in several countries.