The growth came as the broader U.S. economy added 223,000 jobs last month and the unemployment rate ticked down to 3.8%, the lowest level since 2000 and the latest sign that economic growth is picking up steam and pushing more goods through distribution networks.

“We are probably going through one of our largest hiring sprees as a company that we’ve seen in a long time,” said Daniel Sayne, director of sales for Fidelitone Inc., which handles deliveries of heavy goods for Amazon.com Inc., Wayfair Inc. and other e-commerce companies. Heading toward the summer, grills, patio furniture and sporting goods are among the consumer products in high demand, he said.

Mr. Sayne said Fidelitone has expanded its operation significantly in the last year as more online retailers worked out how to sell larger items through online channels. “Retailers and e-commerce companies have invested money in their supply chains to be able to offer those types of services,” he said. “A few years ago you couldn’t go on most of these furniture companies’ websites and buy something, they didn’t offer that.”

The shift in consumer shopping patterns toward e-commerce requires heftier logistics infrastructure and more workers, said Evan Armstrong, president of logistics consulting firm Armstrong & Associates Inc. “As we need more e-commerce fulfillment centers to get goods closer to customers, as we need more capacity for last-mile delivery, that’s impacting all parts of the supply chain,” Mr. Armstrong said.

Consumer-goods and other companies say their freight costs are rising rapidly as they compete for space in capacity-constrained shipping networks. Dollar Tree Inc. said this week its profit margins were hurt by higher freight costs, partly the result of difficulty finding truck drivers in a tight jobs market.

Online freight marketplace DAT Solutions LLC said there were seven loads available on its spot market for every truck.

C.R. England Inc., a large trucking fleet based in Salt Lake City, became the latest in a stream of trucking operators to boost salaries to attract drivers this week, announcing incentive-based packages topping out at a 25% increase in compensation. Coca-Cola Bottling Co. said its Red Classic Services truck subsidiary would increase pay and start offering $5,000 bonuses to get new drivers.

Yong Kim, co-founder of staffing platform Wonolo Inc., said the company has seen a 15 to 20% increase in hourly wage growth in the logistics sector this year.

“Workers are not only chasing after places that offer higher wages, but more importantly ones that provide more flexibility, work-life balance, higher quality of work and career fulfillment,” Mr. Kim said. “We are seeing an interesting empowerment movement among workers.”