It says people have become "screen slaves" and are often working while commuting or after they get home.
The society said poor posture in these environments could lead to back and neck pain.
Unions said people needed to learn to switch off their devices.
An online survey, of 2,010 office workers by the Society found that nearly two-thirds of those questioned continued working outside office hours.
The organisation said people were topping up their working day with more than two hours of extra screentime, on average, every day.
The data suggested that having too much work and easing pressure during the day were the two main reasons for the extra workload.
The chairwoman of the Chartered Society of Physiotherapy, Dr Helena Johnson, said the findings were of "huge concern".
She said: "While doing a bit of extra work at home may seem like a good short-term fix, if it becomes a regular part of your evening routine then it can lead to problems such as back and neck pain, as well as stress-related illness.
"This is especially the case if you’re using hand-held devices and not thinking about your posture. Talk to your employer if you are feeling under pressure."
The general secretary of the Trades Union Congress, Brendan Barber, said: "Excessive work levels are not good for anyone. Overworked employees are not only unlikely to be performing well at work, the stress an unmanageable workload causes is also likely to be making them ill.
"By the time someone is so overloaded they constantly feel the need to put in extra hours every night of the week at home, things have clearly got out of hand.
"Individuals who find themselves unable to leave their work in the office should talk to their managers and learn to switch off their smartphones."