Nanopore sensors have attracted considerable interest for high-throughput sensing of individual nucleic acids and proteins without the need for chemical labels or complex optics. A prevailing problem in nanopore applications is that the transport kinetics of single biomolecules are often faster than the measurement time resolution. Methods to slow down biomolecular transport can be troublesome and are at odds with the natural goal of high-throughput sensing. Here we introduce a low-noise measurement platform that integrates a complementary metal-oxide semiconductor (CMOS) preamplifier with solid-state nanopores in thin silicon nitride membranes. With this platform we achieved a signal-to-noise ratio exceeding five at a bandwidth of 1 MHz, which to our knowledge is the highest bandwidth nanopore recording to date. We demonstrate transient signals as brief as 1 μs from short DNA molecules as well as current signatures during molecular passage events that shed light on submolecular DNA configurations in small nanopores.