Amstrad supplied about 30% of the set-top boxes purchased by Sky last year for use by its pay-TV customers.
The Office of Fair Trading (OFT) said it would examine whether the deal would result in a "substantial lessening of competition" within the market.
Sky is already facing a competition probe into its stake in rival ITV.
The OFT has the power to recommend a full Competition Commission inquiry into Sky's deal with Amstrad, due to be completed later this year.
The Competition Commission, in turn, has the power to potentially block the deal.
The purchase of Amstrad, a computer and electronic hardware firm, would provide BSkyB with an in-house capability to design and develop products vital to its customers.
BSkyB is the largest pay-TV operator in the UK, with more than 8.6 million subscribers.
At the time the deal was announced earlier this month, Amstrad chairman and founder Sir Alan Sugar – who also stars in BBC's The Apprentice show – said he could not imagine a "better home" for his firm than with Sky.
Shares in Pace Micro, one of Amstrad's rivals in the set-top market for digital TV, fell sharply after the deal was announced.