The devices mentioned can detect individual photon strikes with a probability in the tens of percent, so depending on what exactly is meant by “very weak” here a device from this product series may be a reasonable choice. Your target wavelength matches up fairly well with the sensitivity curve of the device, which is helpful.
The photodiode section of this post may offer some useful background info and insight into how devices of this sort are described. That said, getting a bit more detail on the precise nature of the optical situation would be helpful in offering guidance.
Mention of “weaker than the normal ambient light” could be a problem; noticing when somebody lights a candle in a darkened room is much easier than it is outdoors in direct sunlight. Geometry also matters; the smaller your sensor and the further away it is from the light source, the lower the probability that any given photon given off by the source in a random direction will strike the sensor.