Djalali was arrested over a year ago by Iranian secret services, when visiting the capital to deliver a lecture on catastrophe medicine.
Now, he risks being sentenced to death.
"I'm really worried. We have a little bit of hope, but we can't expect anything," said Vida Mehrannia, Djalali's wife.
After 16 months of detention in Iran's Evin Prison, the trial is now set to begin. This follows a three week delay, after the judge complained of illness.
This time round, the Swedish Embassy in Iran applied for a permit to attend the trial.
Patric Nilsson, from the Swedish Ministry for Foreign Affairs, told Swedish Radio that this application was rejected. The Iranian authorities have not explained why.
Nilsson also said that the Ministry intends to act on this case despite the fact that Djalali is only a permanent resident in Sweden, and not a citizen.