Ms Smith said that she had ordered the Migration Advisory Committee to look at the impact that the dependants of immigrants from outside the EU were having on the economy.
"There are all sorts of questions that we might want to ask here – their access to the labour market, the extent to which they as well as the people that they are coming with need to demonstrate the contribution that they are going to make to the UK economy," she told BBC1’s The Andrew Marr Show.
"I haven’t made a decision on that yet. It is important that we base that on evidence and that’s why I have asked the Migration Advisory Committee to do that work."
The move potentially represents a further tightening of the Government’s points-based immigration system for non-EU workers in the face of growing pressure on jobs as the recession worsens.
Ms Smith said that she was also tightening the rules on the most highly qualified workers who do not have to have a job in the UK before they enter the country.
From April, they will have to have at least a master’s degree – rather than a bachelor’s degree – and a previous salary of at least £20,000 to qualify. The Home Office estimates that it will almost halve the numbers coming in from 26,000 to 14,000.
"Migration is important for this country but at a time when we have more people actually looking for work within the UK, it is also economically right that we are more selective about those who come into the country."
The latest announcement comes at a time when Gordon Brown has been under pressure over his controversial promise of "British jobs for British workers".
Although the majority of the people affected by the new measures come from the Indian sub-continent or Africa, Ms Smith strongly denied that they were racist.