Mass-screen-and-treat and targeted mass-drug-administration strategies are being considered as a means to interrupt transmission of Plasmodium falciparum malaria. However, the effectiveness of such strategies will depend on the extent to which current and future diagnostics are able to detect those individuals who are infectious to mosquitoes. We estimate the relationship between parasite density and onward infectivity using sensitive quantitative parasite diagnostics and mosquito feeding assays from Burkina Faso. We find that a diagnostic with a lower detection limit of 200 parasites per microlitre would detect 55% of the infectious reservoir (the combined infectivity to mosquitoes of the whole population weighted by how often each individual is bitten) whereas a test with a limit of 20 parasites per microlitre would detect 83% and 2 parasites per microlitre would detect 95% of the infectious reservoir. Using mathematical models, we show that increasing the diagnostic sensitivity from 200 parasites per microlitre (equivalent to microscopy or current rapid diagnostic tests) to 2 parasites per microlitre would increase the number of regions where transmission could be interrupted with a mass-screen-and-treat programme from an entomological inoculation rate below 1 to one of up to 4. The higher sensitivity diagnostic could reduce the number of treatment rounds required to interrupt transmission in areas of lower prevalence. We predict that mass-screen-and-treat with a highly sensitive diagnostic is less effective than mass drug administration owing to the prophylactic protection provided to uninfected individuals by the latter approach. In low-transmission settings such as those in Southeast Asia, we find that a diagnostic tool with a sensitivity of 20 parasites per microlitre may be sufficient for targeted mass drug administration because this diagnostic is predicted to identify a similar village population prevalence compared with that currently detected using polymerase chain reaction if treatment levels are high and screening is conducted during the dry season. Along with other factors, such as coverage, choice of drug, timing of the intervention, importation of infections, and seasonality, the sensitivity of the diagnostic can play a part in increasing the chance of interrupting transmission.