Concrete is a composite material, so it has no single melting point of its own. Each of the different components of concrete, primarily sand, gravel and cement, has a melting point of its own. Rather than melt concrete, molten lava causes it to rapidly decompose.
According to Oregon State University, lava exists as a liquid between about 1,300 and 2,200 degrees Fahrenheit. At these temperatures, molecules within the concrete called hydroxides decompose into metallic oxides and water. The water quickly escapes as steam, but the oxides can remain solid at very high temperatures. The gravel and other silicates, such as the cement, all have their own individual melting points.