Nanopores are key in portable sequencing and research given their ability to transport elongated DNA or small bioactive molecules through narrow transmembrane channels. Transport of folded proteins could lead to similar scientific and technological benefits. Yet this has not been realised due to the shortage of wide and structurally defined natural pores. Here we report that a synthetic nanopore designed via DNA nanotechnology can accommodate folded proteins. Transport of fluorescent proteins through single pores is kinetically analysed using massively parallel optical readout with transparent silicon-on-insulator cavity chips vs. electrical recordings to reveal an at least 20-fold higher speed for the electrically driven movement. Pores nevertheless allow a high diffusive flux of more than 66 molecules per second that can also be directed beyond equillibria. The pores may be exploited to sense diagnostically relevant proteins with portable analysis technology, to create molecular gates for drug delivery, or to build synthetic cells.