The same association was not seen in infants who share a bed together and researchers were unable to provide a clear explanation for their findings.
One theory suggests that parents who notice wheezing symptoms in their children are more likely to keep them close by at night. This was not confirmed by analysis.
The study of 6,160 mothers and their children in Rotterdam, the Netherlands, showed no link between babies sleeping with parents and an increased risk of wheezing or asthma in the first six years of life.
But bed-sharing at the age of two led to a 42% higher chance of wheezing symptoms at age three to six, and a 57% greater likelihood of being diagnosed with asthma at age six.
Lead researcher Dr Maartje Luijk, from Erasmus University in Rotterdam, said: "The current study shows that there is an association between toddlers who share a bed with their parents at the age of two years and wheezing and asthma in later childhood.
"We postulated that the finding may be explained by parents taking the decision to share a bed with their toddler to monitor their asthma symptoms. However our results found no associations between pre-existing asthma symptoms in the first two years of life and bed-sharing at the age of two years," said Luijk.
"This could suggest that bed-sharing increases the risk of asthma in some way, but this study does not provide causal evidence of this.
"There could be a number of factors at play here. For example, bed-sharing families might be more likely to report wheezing because they are more attentive or aware of their children's breathing.
"Alternatively, families might perceive wheezing as problematic and as something that could lead to sleep problems, which might in turn elicit bed-sharing to better monitor these problems."
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Luijk added: "More research is needed to identify the factors that may impact on the development of asthma through bed-sharing."
The findings are reported in the European Respiratory Journal, whose associate editor Dr Claudia Kueni, from the University of Bern, Switzerland, said: "The study stands out from many others, in that it does not content itself with showing that putative risk factors and health outcome are associated (which means only that they occur more often together than would be expected by chance).
"Rather, the authors investigate temporal relationships to find out if the risk factor, here bed-sharing, might affect the health outcome, in our example asthma.
"Such investigations are only possible when studies measure risk factors and health outcomes at different time points, and results are analysed with appropriate techniques. Although such methods have been known for many years, they remain underused," added Kueni.
The researchers gathered information on children's wheezing and asthma symptoms every year from the age of one to six.
They also assessed sleeping patterns using a parental questionnaire. Bed-sharing was defined as a child sharing a bed with either the mother or both parents.