By a journey to Panama on less than 1 month recommend protection against the following infections:

Diphtheria
Diphtheria is a serious throat infection, which infects from person-to-person through the air. The vaccination should be less than 10 years old otherwise a booster is needed.
Read more about diphteria here.

Yellow fever
Yellow fever is a virus infection, which cause a serious hepatitis. The vaccine provides protection for 10 years after a single injection. Countries where yellow fever is present are entitled to request a valid certificate documenting a vaccination against yellow fever at least 10 days before entry. The certificate is a stamp in the WHO yellow book.
Read more about yellow fever here.

Hepatitis A (infectious hepatitis)
Infectious hepatitis infects through contaminated food and water. Vaccination consists of two injections about 12 months apart, which protects for up to 25 years. The first vaccination protects for 12 months. 
Read more about hepatitis A here.
The hepatitis A vaccine can be combined with the vaccine against hepatitis B

Tetanus
Tetanus is a complication to wounds contaminated by soil. If there has been a vaccination within the past 10 years it is not necessary to give a booster in case of wounds and accidents. Tetanus vaccinations are usually given in combination with diphtheria vaccine. If you are previously vaccinated, the vaccine can be given right up to departure.

Malaria in Panama
The risk of Malaria in Panama is low and limited to the provinces of Darién and San Blas (see map below). Resistance against Chloroquine has been found in these areas and the choice is between: Malarone, Doxycycline or Lariam. Protection against mosquito bites is sufficient in the rest of Panama.
The distribution of malaria can be seen at the map below.
Read more about malaria here.

The information on malaria risk in individual countries are based on the sources found here

Recommended vaccinations Starting Diphtheria 1 day Yellow fever 10 days Hepatitis A (infectious hepatitis) 1 week Tetanus 1 day Malaria in Panama 1-7 days 10 days When to start vaccinations before leaving::