Healthcare has been propping up a shaky labor market. For the first time in over four years, the sector shed thousands of jobs

Despite making up nearly a fifth of the U.S. economy and providing a much-needed set of crutches, the latest healthcare jobs data highlights just how wobbly the labor market is.

Over 28,000 jobs in the healthcare industry were lost in February, according to the  Bureau of Labor Statistics jobs report on Friday, making up nearly one-third of the 92,000 total jobs lost for the month. The dip marks the sector’s first decline in more than four years.

The sector has long been considered...