FedEx Corp.’s split with Amazon.com Inc. is expected to deliver a holiday e-commerce boost to rival United Parcel Service Inc., the U.S. Postal Service and regional package carriers as other providers pick up the slack.

Shipping experts said UPS’s expanded parcel network and the online retail giant’s growing in-house logistics operation would likely provide enough capacity to avoid delivery delays during the busy peak season. Regional delivery operators like OnTrac and LaserShip Inc. could also get a holiday bump from overflow volumes, they said.

“I think Amazon is going to have a little bit of a scramble to fill some of these voids, but there certainly is plenty of capacity in the industry,” said Tim Sailor, founder and principal of Navigo Consulting Group Inc., which advises businesses on shipping costs.

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FedEx announced Wednesday that it hadn’t renewed its contract with Amazon for deliveries through its ground network, adding to an earlier decision to drop Amazon from its Express service.

FedEx has said that Amazon represented less than 1.3% of its total revenue last year, or less than $1 billion. About 80% of that business was in the domestic air shipping contract segment, whose contract with Amazon ended in June, Morgan Stanley analyst Ravi Shanker said in a Wednesday research note.

“In terms of ground volume, FedEx was not doing much with Amazon anyway,” said Cathy Roberson, founder and chief analyst at Logistics Trends & Insights LLC. “They weren’t making their margins with Amazon. Amazon is a very demanding customer, and they can use that to get better rates, to the detriment of their supply-chain partners.”

FedEx declined to comment beyond its statement Wednesday: “This change is consistent with our strategy to focus on the broader e-commerce market.”

An Amazon spokeswoman said FedEx “has been a great partner over the years” and that the company is “confident in our ability to serve customers.”

Some Amazon customers complained about shipping delays during the company’s Prime Day shopping extravaganza in July. The online retailer shipped roughly 100 million packages over the week of the sale, according to an estimate by parcel consulting firm SJ Consulting Group Inc., or more than 14 million packages a day.

“That’s a pretty big number,” said SJ Consulting President Satish Jindel. He said Amazon is rapidly ramping up its network of contract providers to handle last-mile deliveries, and its growing fleet of leased planes will help fill in the gaps from the severed FedEx contract.

“UPS would be delighted to handle” the extra volumes, Mr. Jindel said. The U.S. Postal Service, which he estimates handled 28% of Amazon’s shipments last month, “is going to look at it and say, ‘Thank you, Amazon.’”

A UPS spokesman said the company doesn’t comment on specific customer discussions and that no customer makes up more than 10% of UPS revenue.

Picking up those extra Amazon volumes will heighten carriers’ risks should the online retailer take more business in-house in the future, said Jerry Hempstead, a former parcel-industry executive and principal of e-commerce delivery consultant Hempstead Consulting.

“I’m sure that long-term UPS will be handling less packages,” Mr. Hempstead said. “If Amazon has a truck coming to my house, why would they pay UPS to do that?…They have their own trucks now, they have their own planes, and the writing’s on the wall.”

Write to Jennifer Smith at jennifer.smith@wsj.com