During the height of the outage, here's what Target's website said:
Hours later, Target spokeswoman Jenna Reck said target.com hadn't actually crashed. She said because of the overwhelming number of shoppers, the company slowed down the site in an attempt to accommodate as many people as possible.
She said volume had reached a level "twice as high as our busiest day ever." She acknowledged that some online shoppers may still be having problems.
"As we experience spikes in traffic, our systems place guests in a queue and prompt them to access the site later," she said. "We apologize to guests who experience any delays, we appreciate their patience, and encourage them to try again in a few minutes by refreshing their browser."
This year was the 10th anniversary of Cyber Monday, the Monday following Thanksgiving, which is promoted by online retailers as a day for deep bargains.
The outage angered some would-be shoppers, and shares of Target were down more than 1 percent in Monday afternoon trading. Two years ago, the records of millions of Target customers' accounts were compromised in a Christmastime hacking.
Last week, Target announced a sitewide discount of 15 percent on Cyber Monday and "the first time Target has discounted virtually everything on Target.com." The company also announced several online doorbusters for Nov. 30 and other discounts throughout the week.
Deals included 50 percent off licensed kids' products including "Frozen" and Teenage Mutant Ninja Turtles items and select Sennheiser in-ear headphones.
PayPal problems were also reported in the morning. Around 9:30 a.m. ET, the Ugly Sweater Shop posted the following on its Facebook page:
"Well it appears our payment processor PayPal is down right now. Too many Cyber Monday purchases out there? We will post a notice when it is back up and running, hopefully in a few minutes."
Hours later, a company spokesperson told CNBC: "Earlier today, PayPal experienced a brief, intermittent interruption in our service. We have resolved the issue and customers can pay with PayPal on Cyber Monday."
Retailers experienced problems with the websites even before Cyber Monday.
Upscale retailer Neiman Marcus' website was unavailable most of Friday, according to website performance monitor Catchpoint Systems.
About 121 million shoppers were expected to shop online on Cyber Monday, down slightly from the 126.9 million last year, according to the National Retail Federation.
— Reuters contributed to this report.