Manchester-based Prolific North, which has been using its logo since it launched in January 2013, said even an "amateur eye" could see the similarity.
Editor David Prior said readers alerted him to the new Netflix icon, which was unveiled on Monday on the company's social media accounts.
Netflix has declined to comment.
An article highlighting the similarity on Prolific North's website said some people "found the red strip, folded into an 'N', strikingly familiar".
"They say imitation is the sincerest form of flattery, so I suppose we should all be feeling fabulous at Prolific North this week," it read.
Mr Prior said this "may or may not cause problems in the future" and was "probably completely accidental" but the company would not consider changing their "very well-established logo".
Prolific North's logo was designed by Origin and reworked by Don't Panic in March 2015.
A publishing company is taking legal advice after it described a new Netflix logo as bearing more than a passing resemblance to its own.