This depends what you are measuring.
The metric system uses prefixes to change the size of units.
Litres can have the prefix milli. Millilitres are a thousandth of a litre.
Similarly, millimetres are a thousandth of a metre.
Other prefixes are:
micro = 1/1 000 000; 10-6
nano = 10-9
pico = 10-12
femto = 10-15
There is no smallest metric unit of mass.
Mass is only in kg (kilograms).
But there might be several prefixes depending is value greater or smaller then kg.
So you can use milligram (10^-3), microgram (10^-6), nanogram (10^-9) etc...
Smallest prefix from a SI table would be yoctogram (10^-24 kg) but since it's very rare it can be just used 10^-24 kg or, by the same principle, you can use smaller (or every other prefix) as 10^-28, 10^-16 regardless prefix name.
The smallest unit of weight that has a name is a picogram, which is 1/1000th of a nanogram.
1 gigatonne(Gt)=1 000 000 000 000 000 g
1 megatonne(Mt)=1 000 000 000 000 g
1 tonne(t)=1 000 000 g
1 kilogram(kg)=1 000 g
1 gram(g)=1 g
1 milligram(mg)=0.001 g
1 microgram(µg)=0.000 001 g
1 nanogram(ng)=0.000 000 001 g
1 picogram(pg)=0.000 000 000 001g
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