Boxed.com — the bulk grocery site that’s been dubbed “Costco for millennials” — is taking a page from Amazon’s playbook.

For the first time, the 4-year-old Web retailer is introducing a membership fee for customers who want lower shipping fees and deeper discounts.

The program, Boxed Up, launches on Monday with a $49 annual fee. Benefits include 2-percent cash rewards on purchases and free priority shipping for orders as low as $19.99 compared with the current minimum of $49. Corporate clients also are eligible.

Members also will get exclusive deals including a 15-percent discount on Boxed’s line of Prince & Spring private-label goods. They’ll also get 25 percent off items like Capri Sun, LifeWater and Starbucks Cold Brew.

“Boxed Up is more like Amazon Prime than a Costco membership,” Boxed’s founder and chief executive Chieh Huang told The Post, noting that Boxed will still be open to customers who don’t buy a membership.

“As long as I’m at the helm of the company, Boxed will be free to use,” Huang said. The CEO added that “The vast majority of customers will get their typical free experience.”

In January, The Post reported that Huang met with Amazon executives to discuss an investment or acquisition.

Boxed customers on average spend $100 per transaction, buying between 8 and 10 products. The “biggest wild card” with the Boxed Up program, Huang said, is that customers might “check out when they’ve spent $19.99.”