Amazon's stunning growth in the internet advertising market will boost the company's shares, according to Piper Jaffray.

The firm reaffirmed its overweight rating for the internet giant's stock, predicting its ad business profits will surpass its cloud computing income by 2021.

"While the Street has been focusing on the trajectory of core retail, growth of AWS, and new categories such as grocery & pharma, Amazon's advertising business has been quietly growing into a massive driver of current and future profitability," analyst Michael Olson said in a note to clients Monday. "By 2021, we believe it is likely that advertising operating income will exceed AWS. … Investors should be focused on Amazon advertising now; this is a major driver to results and valuation today and continuing in the coming quarters & years."

Amazon shares closed up less than 1 percent Monday after the report.

Olson reiterated his $2,100 price target for Amazon shares, representing 11 percent upside to Friday's close.

The analyst estimates Amazon's ad business operating income will grow to $16 billion in 2021 versus $15 billion for Amazon Web Services that year. He believes Amazon already has product search market share "well above" 50 percent. Olson noted the "Other" segment, where Amazon's ad business resides, grew sales 72 percent in the second quarter.

"Being the world's largest product search engine has its advantages and Amazon is starting to leverage them," he said. "Advertising will be a driver to watch, as the retail industry continues to live or die by the shift to direct-to-consumer & digital channels and real estate on Amazon, more than any other digital company, may have a direct line of sight on the multi-billion dollar 'trade promotion / merchandising' budgets of many marketers."

Amazon shares have rallied 61 percent this year through Friday, compared with the market's 6 percent gain.