Consuming more than four portions a week is a risk, suggests the study of nearly 1,000 French people, published in the journal Thorax.
The researchers believe it could be a preservative called nitrite used in meats such as sausages, salami and ham that aggravates the airways.
But experts say the link has not been proved and more investigations are needed.
Rather than worry about one type of food, people should be eating a healthy and varied diet, they advise.
Processed meat has already been linked with cancer.
Experts say people should eat no more than 70g a day of red and processed meat for good health.
That's about one sausage plus a rasher of bacon a day.
The people in the study had been taking part in a French survey about food and health, spanning a decade from 2003 to 2013.
Around half of them were asthma patients. The rest - the control subjects - had no history of the condition.
The survey looked specifically at asthma symptoms - breathlessness, wheeze, chest tightness - and intake of cured meat: a single portion was two slices of ham, one sausage or two slices of salami.
Among the people with asthma, higher meat consumption was linked with a worsening of their lung symptoms.
People who said they consumed more than four portions a week - eight slices of ham or four sausages, for example - had the biggest deterioration of their asthma by the end of the study.
The experts stress that their work cannot prove diet is definitely to blame. There are lots of factors in a person's life that can make their asthma worse.
The researchers tried to eliminate the most obvious ones, controlling for things like obesity, and the link between processed meat and worsening asthma remained.
Dr Erika Kennington, Head of Research at Asthma UK says: "Although certain foods can be triggers for allergies in some people, there is no specific dietary advice to manage asthma symptoms generally. For most people with asthma, healthy eating advice is exactly the same as it is for everyone else: follow a balanced diet that includes plenty of fresh and unprocessed food and is low in sugar, salt and saturated fat."
Catherine Collins of the British Dietetic Association recommended "a varied and Mediterranean-style diet", containing plenty of fresh produce, "whether you have asthma or not."