Background Globally the incidence of cancer is about 19.3 million new cases per year. Chemotherapy is among the standard treatments for cancer but neutropenia and febrile neutropenia are the most common side effects. Objective To assess the incidences of chemotherapy-induced neutropenia, febrile-neutropenia and associated factors in solid cancer patients attending Oncology unit of St. Paul Hospital Millennium Medical College in Addis Ababa, Ethiopia. Methods In this institution-based longitudinal study conducted from February to September, 2020 at one of the largest teaching and referral hospitals of Ethiopia, 101 patients who were diagnosed with any type of solid cancer were recruited using convenience sampling method. Patients were followed-up until they completed five cycles of chemotherapy. Data were analyzed using SPSS version 23 software. Paired sample t -test was used to compare the pre- and post-treatment results. Chi-squared test was employed to determine associated factors of neutropenia, and p-values less than 0.05 were taken as statistically significant. Results Of the total 101 participants, 98 were eligible per inclusion criteria and 6 (6.1%) of them died during the study period. The age of the participants ranged from 16–84 years with a mean age of 45. Of them, 48 (49.0%) were in the age group of 16–44 years, 73 (74.5%) were female, 66 (67.3%) were married, and 42.9% attained primary education. Among 92 patients, the incidence of neutropenia was 65 (70.7%) and the incidence of febrile neutropenia was 46 (50.0%). Adriamycin + cyclophosphamide and Adriamycin + cyclophosphamide + paclitaxel were the most commonly used anti-cancer treatments in this study. None of the tested factors were associated with chemo-induced neutropenia. Conclusion More than two thirds of the patients had chemotherapy associated neutropenia while half of the patients had febrile neutropenia; close monitoring of such patients is warranted.