Robin Manthie and her husband have been looking for their first home in Minneapolis since last May. They thought this spring would bring a flood of inventory, making their search easier. But by most measures it is getting tougher.

The inventory of homes for sale in Minneapolis dropped by about 25% in February compared with a year earlier, while the median sale price rose by 7.6% to $223,000, according to the Minneapolis Area Association of Realtors. That’s on par with the national median home price of $228,400. The average...