The seasonally-adjusted Absa Purchasing Managers' Index (PMI) was at 53.0 points in January, almost unchanged from 53.1 in December and remaining above the 50-point mark that separates expansion from contraction.
The survey showed that the business activity index improved in comparison to the previous month despite rolling power cuts, which held back production and affected new sales orders.
"Should this translate into actual production growth, it would be a promising start to the year for the struggling sector," Absa said in a statement.
Absa added that continued activity growth would require a sustained improvement in demand and most likely a move to less intense stages of power outages.
Eskom has implemented power cuts every day this year, after a record number of days with outages last year. On Tuesday, it ramped up power cuts to the highest level on record.